JAM 2015: General Instructions during Examination
|
|
- Beatrix May
- 5 years ago
- Views:
Transcription
1 JAM 05 JAM 05: Geeral Istructos durg Examato. Total durato of the JAM 05 examato s 80 mutes.. The clock wll be set at the server. The coutdow tmer at the top rght corer of scree wll dsplay the remag tme avalable for you to complete the examato. Whe the tmer reaches zero, the examato wll ed by tself. You eed ot termate the examato or submt your paper. 3. Ay useful data requred for your paper ca be vewed by clckg o the Useful Data butto that appears o the scree. 4. Use the scrbble pad provded to you for ay rough work. Submt the scrbble pad at the ed of the examato. 5. You are allowed to use oly your ow o-programmable calculator. 6. The Questo Palette dsplayed o the rght sde of scree wll show the status of each questo usg oe of the followg symbols: 7. The Marked for Revew status for a questo smply dcates that you would lke to look at that questo aga. If a questo s 'aswered, but marked for revew', the the aswer wll be cosdered for evaluato uless the status s modfed by the caddate. Navgatg to a Questo : 8. To aswer a questo, do the followg: a. Clck o the questo umber the Questo Palette to go to that questo drectly. b. Select the aswer for a multple choce type questo ad for the multple select type questo. Use the vrtual umerc keypad to eter the aswer for a umercal type questo. c. Clck o Save & Next to save your aswer for the curret questo ad the go to the ext questo. d. Clck o Mark for Revew & Next to save ad to mark for revew your aswer for the curret questo, ad the go to the ext questo. Cauto: Note that your aswer for the curret questo wll ot be saved, f you avgate to aother questo drectly by clckg o a questo umber wthout savg the aswer to the prevous questo. 9. You ca vew all the questos by clckg o the Questo Paper butto. Ths feature s provded, so that f you wat you ca just see the etre questo paper at a glace. Aswerg a Questo : 0. Procedure for aswerg a multple choce questo (MCQ): a. Choose the aswer by selectg oly oe out of the 4 choces (A,B,C,D) gve below the questo ad clck o the bubble placed before the selected choce. MS /8
2 JAM 05 b. To deselect your chose aswer, clck o the bubble of the selected choce aga or clck o the Clear Respose butto. c. To chage your chose aswer, clck o the bubble of aother choce. d. To save your aswer, you MUST clck o the Save & Next butto.. Procedure for aswerg a multple select questo (MSQ): a. Choose the aswer by selectg oe or more tha oe out of the 4 choces (A,B,C,D) gve below the questo ad clck o the checkbox(es) placed before each of the selected choce (s). b. To deselect oe or more of your selected choce(s), clck o the checkbox(es) of the choce(s) aga. To deselect all the selected choces, clck o the Clear Respose butto. c. To chage a partcular selected choce, deselect ths choce that you wat to chage ad clck o the checkbox of aother choce. d. To save your aswer, you MUST clck o the Save & Next butto.. Procedure for aswerg a umercal aswer type (NAT) questo: a. To eter a umber as your aswer, use the vrtual umercal keypad. b. A fracto (e.g or -.3) ca be etered as a aswer wth or wthout '0' before the decmal pot. As may as four decmal pots, e.g or or or.8 ca be etered. c. To clear your aswer, clck o the Clear Respose butto. d. To save your aswer, you MUST clck o the Save & Next butto. 3. To mark a questo for revew, clck o the Mark for Revew & Next butto. If a aswer s selected (for MCQ ad MSQ types) or etered (for NAT) for a questo that s Marked for Revew, that aswer wll be cosdered the evaluato uless the status s modfed by the caddate. 4. To chage your aswer to a questo that has already bee aswered, frst select that questo ad the follow the procedure for aswerg that type of questo as descrbed above. 5. Note that ONLY those questos for whch aswers are saved or marked for revew after aswerg wll be cosdered for evaluato. Choosg a Secto : 6. Sectos ths questo paper are dsplayed o the top bar of the scree. All sectos are compulsory. 7. Questos a secto ca be vewed by clckg o the ame of that secto. The secto you are curretly vewg wll be hghlghted. 8. To select aother secto, smply clck the ame of the secto o the top bar. You ca shuffle betwee dfferet sectos ay umber of tmes. 9. Whe you select a secto, you wll oly be able to see questos ths Secto, ad you ca aswer questos the Secto. 0. After clckg the Save & Next butto for the last questo a secto, you wll automatcally be take to the frst questo of the ext secto sequece.. You ca move the mouse cursor over the ame of a secto to vew the aswerg status for that secto. MS /8
3 JAM 05 JAM 05 Examato MS: Mathematcal Statstcs Durato: 80 mutes Maxmum Marks: 00 Read the followg structos carefully.. To log, eter your Regstrato Number ad Password provded to you. Kdly go through the varous coloured symbols used the test ad uderstad ther meag before you start the examato.. Oce you log ad after the start of the examato, you ca vew all the questos the questo paper, by clckg o the Questo Paper butto the scree. 3. Ths test paper has a total of 60 questos carryg 00 marks. The etre questo paper s dvded to three sectos, A, B ad C. All sectos are compulsory. Questos each secto are of dfferet types. 4. Secto A cotas Multple Choce Questos (MCQ). Each MCQ type questo has four choces out of whch oly oe choce s the correct aswer. Ths secto has 30 Questos ad carry a total of 50 marks. Q. Q.0 carry mark each ad Questos Q. Q.30 carry marks each. 5. Secto B cotas Multple Select Questos (MSQ). Each MSQ type questo s smlar to MCQ but wth a dfferece that there may be oe or more tha oe choce(s) that are correct out of the four gve choces. The caddate gets full credt f he/she selects all the correct choces oly ad o wrog choces. Ths secto has 0 Questos ad carry marks each wth a total of 0 marks. 6. Secto C cotas Numercal Aswer Type (NAT) questos. For these NAT type questos, the aswer s a real umber whch eeds to be etered usg the vrtual umercal keypad o the motor. No choces wll be show for these type of questos. Ths secto has 0 Questos ad carry a total of 30 marks. Q. Q.0 carry mark each ad Questos Q. Q.0 carry marks each. 7. Depedg upo the JAM test paper, there may be useful commo data that may be requred for aswerg the questos. If the paper has such useful data, the same ca be vewed by clckg o the Useful Data butto that appears at the top, rght had sde of the scree. 8. The computer allotted to you at the examato cetre rus specalzed software that permts oly oe choce to be selected as aswer for multple choce questos usg a mouse, oe or more tha oe choces to be selected as aswer for multple select questos usg a mouse ad to eter a sutable umber for the umercal aswer type questos usg the vrtual umerc keypad ad mouse. 9. Your aswers shall be updated ad saved o a server perodcally ad also at the ed of the examato. The examato wll stop automatcally at the ed of 80 mutes. 0. Multple choce questos (Secto-A) wll have four choces agast A, B, C, D, out of whch oly ONE choce s the correct aswer. The caddate has to choose the correct aswer by clckg o the bubble ( ) placed before the choce.. Multple select questos (Secto-B) wll also have four choces agast A, B, C, D, out of whch ONE OR MORE THAN ONE choce(s) s /are the correct aswer. The caddate has to choose the correct aswer by clckg o the checkbox ( ) placed before the choces for each of the selected choce(s).. For umercal aswer type questos (Secto-C), each questo wll have a umercal aswer ad there wll ot be ay choces. For these questos, the aswer should be etered by usg the mouse ad the vrtual umercal keypad that appears o the motor. 3. I all questos, questos ot attempted wll result zero mark. I Secto A (MCQ), wrog aswer wll result NEGATIVE marks. For all mark questos, /3 marks wll be deducted for each wrog aswer. For all marks questos, /3 marks wll be deducted for each wrog aswer. I Secto B (MSQ), there s NO NEGATIVE ad NO PARTIAL markg provsos. There s NO NEGATIVE markg Secto C (NAT) as well. MS 3/8
4 JAM No-programmable calculators are allowed but sharg of calculators s ot allowed. 5. Moble phoes, electroc gadgets other tha calculators, charts, graph sheets, ad mathematcal tables are NOT allowed the examato hall. 6. You ca use the scrbble pad provded to you at the examato cetre for all your rough work. The scrbble pad has to be retured at the ed of the examato. Declarato by the caddate: I have read ad uderstood all the above structos. I have also read ad uderstood clearly the structos gve o the admt card ad shall follow the same. I also uderstad that case I am foud to volate ay of these structos, my caddature s lable to be cacelled. I also cofrm that at the start of the examato all the computer hardware allotted to me are proper workg codto. MS 4/8
5 JAM 05 E P A Specal Istructos / Useful Data Set of all real umbers x,, :,,,, x x Expectato of the radom varable Probablty of the evet A Ua, b Cotuous uform dstrbuto o, ab, ab N, Normal dstrbuto wth mea ad varace B, p Posso Bomal dstrbuto wth trals ad success probablty p Posso dstrbuto wth parameter Geom p Geometrc dstrbuto wth parameter p, whose probablty mass x P x p p, x,, fucto s gve by Gamma, Gamma dstrbuto wth parameters ad, whose probablty x x e, x 0, desty fucto s gve by f( x) ( ) 0, otherwse. P The sequece of radom varables coverges probablty to the radom varable d The sequece of radom varables coverges dstrbuto to the radom varable! Bomal coeffcet, equal to x x!( x)! log x Natural logarthm of x I Idetty matrx Cumulatve dstrbuto fucto of N (0,) x Specal values , , e.78, 3.4 log MS 5/8
6 JAM 05 Q. Q.0 carry oe mark each. SECTION A MULTIPLE CHOICE QUESTIONS (MCQ) Q. Let,, be a radom sample from a populato wth probablty desty fucto x e, x 0, f ( x) 0, otherwse, where 0 s a ukow parameter. The, the uformly mmum varace ubased estmator for s Q. Let,, 00 be depedet ad detcally dstrbuted 0, 98 The correlato betwee ad s equal to 00 3 N radom varables Q.3 Cosder the problem of testg H : 0 0 agast H : based o a sgle observato from U, populato. The power of the test "Reject H0 f " s MS 6/8
7 JAM 05 Q.4 The probablty mass fucto of a radom varable s gve by P x k, x 0,,,, x where k s a costat. The momet geeratg fucto M (t) s t e t e e t t e Q.5 Suppose A ad B are evets wth P A PB c P B A B s equal to c 0.5, 0.4 ad P AB 0.. The Q.6 Let,, be a radom sample from a, Gamma populato, where 0 s a kow costat. The rejecto rego of the most powerful test for H : 0 agast H : form s of the K K K K Q.7 Whch of the followg s NOT a lear trasformato? T : T : T : T : 3 defed by T( x, y, z) ( x, z) 3 3 defed by T( x, y, z) ( x, y -, z) defed by T( x, y) ( x, y - x) defed by T( x, y) ( y, x) Q.8 If a sequece x s mootoe ad bouded, the there exsts a subsequece of x that dverges there may exst a subsequece of x that s ot mootoe all subsequeces of x coverge to the same lmt there exst at least two subsequeces of x whch coverge to dstct lmts MS 7/8
8 JAM 05 Q.9 Let f : be defed by f( x) x( x)( x ). The f s oe-oe ad oto f s ether oe-oe or oto f s oe-oe but ot oto f s ot oe-oe but oto Q.0 Whch of the followg statemets s true for all real umbers x? x e x x e x x e x x e x Q. Q. 30 carry two marks each. Q. Let,, be a radom sample from a Posso populato, where 0 s ukow. The Cramer-Rao lower boud for the varace of ay ubased estmator of g( ) e equals ( ) e ( ) e ( ) e ( ) e Q. Let ad Y be two depedet radom varables such that U0, ad Y U, 3 The P Y equals Q.3 There are two boxes, each cotag two compoets. Each compoet s defectve wth probablty /4, depedet of all other compoets. The probablty that exactly oe box cotas exactly oe defectve compoet equals Q.4 Cosder a ormal populato wth ukow mea ad varace 9. To test H : 0 0 agast H : 0, a radom sample of sze 00 s take. Based o ths sample, the test of the form K rejects the ull hypothess at 5% level of sgfcace. The, whch of the followg s a possble 95% cofdece terval for? 0.488, , , ,.96 MS 8/8
9 JAM 05 Q.5 Let,, be a radom sample from a populato wth probablty desty fucto ( ) x, 0 x, f ( x) 0, otherwse, where 0 s ukow. The maxmum lkelhood estmator of s log log log log log Q.6 Let,, be a radom sample from a populato wth probablty desty fucto x x e, x 0, f ( x) 0, otherwse, where 0 s ukow. The, a cosstet estmator for s Q.7 Let the probablty desty fucto of a radom varable be gve by x f( x) e, x. If E( ), the 4 e ad e 4 ad e 4 ad e 4 ad x MS 9/8
10 JAM 05 Q.8 Let be a sgle observato from a populato havg a expoetal dstrbuto wth mea. Cosder the problem of testg H : 0 agast H : 4. For the test wth rejecto let PType Ierror ad P rego 3, TypeIIerror. The 6 e ad e ad e 6 e e ad 6 e ad e e 6 Q.9 Let Y be a expoetal radom varable wth mea, where 0. The codtoal dstrbuto of gve Y has Posso dstrbuto wth mea Y. The, the varace of s Q cashew uts are mxed thoroughly flour. The etre mxture s dvded to 000 equal parts ad each part s used to make oe bscut. Assume that o cashews are broke the process. A bscut s pcked at radom. The probablty that t cotas o cashew uts s betwee 0 ad 0. betwee 0. ad 0. betwee 0. ad 0.3 betwee 0.3 ad 0.4 Q. Suppose,, are depedet radom varables ad k s ukow. The maxmum lkelhood estmator for s N 0, k, k,,, where k k ( k ) k k k k k k k k Q. Let,, 0 be depedet ad detcally dstrbuted 5,5 dstrbuto of the radom varable Y log 5 0 s U radom varables. The, the MS 0/8
11 JAM 05 Q.3 Let f : be a dfferetable fucto so that f( x) f( x) 0 for all x. The, whch of the followg s ecessarly true? f s a creasg fucto f s a decreasg fucto f s a creasg fucto f s a decreasg fucto Q.4 Let M be the matrx 3. Whch of the followg matrx equatos does M satsfy? M M I M M M M M M 3 0 M M I 5 0 Q.5 If the determat of a matrx A s zero, the rak( A) the trace of A s zero zero s a egevalue of A x 0 s the oly soluto of Ax 0 Q.6 Let f :(0, ) be gve by The, the umber of roots of f s f( x) logx x. 0 3 Q.7 The umber of dstct real values of x for whch the matrx x x x s sgular s 3 fte MS /8
12 JAM 05 Q.8 Suppose f : The h () s equal to s a cotuous fucto. Defe h : x x hx ( ) f( uvdudv, ). 0 0 by f (,) f(, 0) f(0,) f (,) tt dt f (, t) f( t,) dt 0 0 Q.9 Let A be a 5 3 real matrx of rak. Let space of. A Let S x Ax b 3 x0 as the set x0 V x0 v: v V 5 b be a o-zero vector that s the colum 3 :. Defe the traslato of a subspace V of. The S s the empty set S has oly oe elemet S s a traslato of a dmesoal subspace S s a traslato of a dmesoal subspace 3 by Q.30 Let f : be a dfferetable fucto whose dervatve s cotuous. The lm ( ) x f( x) dx 0 s equal to 0 s equal to 0 f x dx s fte s equal to f () MS /8
13 JAM 05 Q. Q. 0 carry two marks each. Q. Suppose, SECTION - B MULTIPLE SELECT QUESTIONS (MSQ) a b are sequeces such that a 0, b 0 for all. Gve that a coverges ad b dverges, whch of the followg statemets s (are) ecessarly FALSE? ( a b) coverges a coverges b b coverges a ab coverges Q. Cosder the ordary dfferetal equato dy x y x for 0. dx x Whch of the followg s (are) soluto(s) to the above? x x yx ( ) yx ( ) x x yx ( ) 0 yx ( ) x Q.3 Let f :[0,] be a cotuous fucto such that The f attas the value 0 at least twce [0,] f attas the value 0 exactly twce [0,] f attas the value 0 exactly oce [0,] the rage of f s [,] f(0), f, f(). Q.4 Let f :. Defe g : by The g s eve for all f g s odd for all f g s eve f f s eve g s eve f f s odd g( x) f( x) f( x) f( x). MS 3/8
14 JAM 05 Q.5 Whch of the followg matrces ca be the varace-covarace matrx of a radom vector? Q.6 Let,, be a radom sample from a N (,) populato, where s ukow. Whch of the followg statstcs s (are) suffcet for?,, 3, 4,, 3, 4 Q.7 Let,, be a radom sample from a T N(, ) dstrbuto, where 0 s ukow. Let ad T Whch of the followg statemets s (are) correct? T s ubased for T s ubased for T s cosstet for T s cosstet for. Q.8 Suppose ad Y are depedet ad detcally dstrbuted radom varables wth fte varace Whch of the followg expressos s (are) equal to. E EY E Y? Y E E Y m E a a MS 4/8
15 JAM 05 Q.9 Let,, be a sequece of depedet ad detcally dstrbuted radom varables wth mea ad varace 4. Whch of the followg statemets s (are) true? P P 4 d N(0,) E 4 for all Q.0 Let,, (assume ) be a radom sample from a, N populato where ad 0 are ukow. Whch of the followg statemets s (are) true? The maxmum lkelhood estmator of attas the Cramer-Rao lower boud The uformly mmum varace ubased estmator of attas the Cramer-Rao lower boud The maxmum lkelhood estmator of s a ubased estmator of The relatve effcecy of the maxmum lkelhood estmator of wth respect to the uformly mmum varace ubased estmator of s strctly less tha MS 5/8
16 JAM 05 SECTION C NUMERICAL ANSWER TYPE (NAT) Q. Q. 0 carry oe mark each. Q. Let ad Y be depedet expoetally dstrbuted radom varables wth meas 4 ad 6 respectvely. Let Z m, Y. The EZ. Q. Let be a (0.4) Geom radom varable. The P 5. Q.3 s a sgle observato from a B, p populato, where 5,45 p s ukow. If the observed value of s 0, the the maxmum lkelhood estmator of p s. Q.4 s a radom varable wth desty E. x f( x) e, x. The 4 Q.5 A system comprsg of detcal compoets works f at least oe of the compoets works. Each of the compoets works wth probablty 0.8, depedet of all other compoets. The mmum value of for whch the system works wth probablty at least 0.97 s. Q.6 Let be a ormal radom varable wth mea ad varace 4, ad ga Pa a The value of a that maxmzes g( a) s. ( ). Q.7 The volume of the sold formed by revolvg the curve y x betwee x 0 ad x about the x -axs s equal to. Q.8 Let [ x ] be the greatest teger less tha or equal to x. The [ xdx ]. Q.9 The umber of real solutos of the equato s. 3 x x x MS 6/8
17 JAM 05 Q.0 Let f : be a o-costat, three tmes dfferetable fucto. If tegers, the f (). f for all Q. Q. 0 carry two marks each. Q. Let Y ~ U 0,. The codtoal probablty desty fucto of gve Y s The E. f Y x y, f 0 x y, y 0, otherwse. Q. The probablty desty fucto of a radom varable s gve by, f x, 4 f x, otherwse. 4x The P. Q.3 Let,, dstrbuto. The 34 lm P. be depedet ad detcally dstrbuted radom varables wth U 0, Q.4 Based o 0 observatos x y x y,,,,, the followg values are obtaed x x y xy 6, 4, 9 ad 0. For, the predcted value of Y based o a least squares ft of a lear regresso model of Y o s. MS 7/8
18 JAM 05 Q.5 The cumulatve dstrbuto fucto of a radom varable s gve by The P 0, f x 0, Fx 4 xx, f 0 x, 4 6, f x Q.6 The probablty desty fucto f ( x ) of a radom varable s symmetrc about 0. The x f ( u) du dx. Q.7 The legth of the curve y 4 x from x to x s equal to. Q.8 The system of equatos x yz x 3yz 5 4x 7ycz6 does NOT have a soluto. The, the value of c must be equal to. Q.9 Let y( x ) be a soluto to the dfferetal equato y'' y' y 0, y(0) ad y'(0). The lm yx ( ). x Q.0 The area of the rego the frst quadrat eclosed by the curves y 0, y x ad equal to. y s x END OF THE QUESTION PAPER MS 8/8
19 JAM 05 Aswer Keys for the Test Paper: Mathematcal Statstcs (MS) Secto A - MCQ Multple Choce Questos Secto B - MSQ Multple Select Questos Secto C - NAT Numercal Aswer Type Questos Q. No. Key Marks Q. No. Key Marks Q. No. Rage Marks C A;C 0. to 0. B A;B;C to B 3 A 3 0. to 0. 4 A 4 C;D 4 to 5 B 5 A 5 3 to 3 6 A 6 A;B;C;D 6 to 7 B 7 B;C;D 7.04 to.05 8 C 8 A;C;D 8 0 to 0 9 D 9 A;C;D 9 to 0 B 0 A;B 0 0 to 0 A 0.5 to 0.5 C 0.5 to C 3 to 4 C 4.40 to.45 5 C to A 6 to 7 A to A 8-7 to -7 9 D 9 0 to 0 0 B to 0.9 C C 3 D 4 B 5 C 6 C 7 B 8 D 9 C 30 D
Special Instructions / Useful Data
JAM 6 Set of all real umbers P A..d. B, p Posso Specal Istructos / Useful Data x,, :,,, x x Probablty of a evet A Idepedetly ad detcally dstrbuted Bomal dstrbuto wth parameters ad p Posso dstrbuto wth
More informationUNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postpoed exam: ECON430 Statstcs Date of exam: Jauary 0, 0 Tme for exam: 09:00 a.m. :00 oo The problem set covers 5 pages Resources allowed: All wrtte ad prted
More informationSummary of the lecture in Biostatistics
Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the
More informationChapter 14 Logistic Regression Models
Chapter 4 Logstc Regresso Models I the lear regresso model X β + ε, there are two types of varables explaatory varables X, X,, X k ad study varable y These varables ca be measured o a cotuous scale as
More informationUNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON430 Statstcs Date of exam: Frday, December 8, 07 Grades are gve: Jauary 4, 08 Tme for exam: 0900 am 00 oo The problem set covers 5 pages Resources allowed:
More informationChapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
More informationENGI 3423 Simple Linear Regression Page 12-01
ENGI 343 mple Lear Regresso Page - mple Lear Regresso ometmes a expermet s set up where the expermeter has cotrol over the values of oe or more varables X ad measures the resultg values of aother varable
More informationEconometric Methods. Review of Estimation
Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators
More information22 Nonparametric Methods.
22 oparametrc Methods. I parametrc models oe assumes apror that the dstrbutos have a specfc form wth oe or more ukow parameters ad oe tres to fd the best or atleast reasoably effcet procedures that aswer
More informationQualifying Exam Statistical Theory Problem Solutions August 2005
Qualfyg Exam Statstcal Theory Problem Solutos August 5. Let X, X,..., X be d uform U(,),
More informationLecture 3. Sampling, sampling distributions, and parameter estimation
Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called
More informationLecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model
Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The
More informationCHAPTER VI Statistical Analysis of Experimental Data
Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca
More informationTHE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY 3 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA PAPER I STATISTICAL THEORY & METHODS The Socety provdes these solutos to assst caddates preparg for the examatos future years ad
More informationSimple Linear Regression
Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato
More informationSTK4011 and STK9011 Autumn 2016
STK4 ad STK9 Autum 6 Pot estmato Covers (most of the followg materal from chapter 7: Secto 7.: pages 3-3 Secto 7..: pages 3-33 Secto 7..: pages 35-3 Secto 7..3: pages 34-35 Secto 7.3.: pages 33-33 Secto
More information{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:
Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed
More informationENGI 4421 Joint Probability Distributions Page Joint Probability Distributions [Navidi sections 2.5 and 2.6; Devore sections
ENGI 441 Jot Probablty Dstrbutos Page 7-01 Jot Probablty Dstrbutos [Navd sectos.5 ad.6; Devore sectos 5.1-5.] The jot probablty mass fucto of two dscrete radom quattes, s, P ad p x y x y The margal probablty
More informationLecture Notes Types of economic variables
Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte
More informationX X X E[ ] E X E X. is the ()m n where the ( i,)th. j element is the mean of the ( i,)th., then
Secto 5 Vectors of Radom Varables Whe workg wth several radom varables,,..., to arrage them vector form x, t s ofte coveet We ca the make use of matrx algebra to help us orgaze ad mapulate large umbers
More informationX ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
More informationTHE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA PAPER II STATISTICAL THEORY & METHODS The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for
More informationSTA 105-M BASIC STATISTICS (This is a multiple choice paper.)
DCDM BUSINESS SCHOOL September Mock Eamatos STA 0-M BASIC STATISTICS (Ths s a multple choce paper.) Tme: hours 0 mutes INSTRUCTIONS TO CANDIDATES Do ot ope ths questo paper utl you have bee told to do
More informationTHE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE
THE ROYAL STATISTICAL SOCIETY 00 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for the
More informationFunctions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
More informationChapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
More informationMultivariate Transformation of Variables and Maximum Likelihood Estimation
Marquette Uversty Multvarate Trasformato of Varables ad Maxmum Lkelhood Estmato Dael B. Rowe, Ph.D. Assocate Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Copyrght 03 by Marquette Uversty
More informationRandom Variables and Probability Distributions
Radom Varables ad Probablty Dstrbutos * If X : S R s a dscrete radom varable wth rage {x, x, x 3,. } the r = P (X = xr ) = * Let X : S R be a dscrete radom varable wth rage {x, x, x 3,.}.If x r P(X = x
More informationLecture Note to Rice Chapter 8
ECON 430 HG revsed Nov 06 Lecture Note to Rce Chapter 8 Radom matrces Let Y, =,,, m, =,,, be radom varables (r.v. s). The matrx Y Y Y Y Y Y Y Y Y Y = m m m s called a radom matrx ( wth a ot m-dmesoal dstrbuto,
More informationDiscrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand DIS 10b
CS 70 Dscrete Mathematcs ad Probablty Theory Fall 206 Sesha ad Walrad DIS 0b. Wll I Get My Package? Seaky delvery guy of some compay s out delverg packages to customers. Not oly does he had a radom package
More informationρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
More informationECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity
ECONOMETRIC THEORY MODULE VIII Lecture - 6 Heteroskedastcty Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur . Breusch Paga test Ths test ca be appled whe the replcated data
More informationLecture 3 Probability review (cont d)
STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto
More informationSimulation Output Analysis
Smulato Output Aalyss Summary Examples Parameter Estmato Sample Mea ad Varace Pot ad Iterval Estmato ermatg ad o-ermatg Smulato Mea Square Errors Example: Sgle Server Queueg System x(t) S 4 S 4 S 3 S 5
More informationPoint Estimation: definition of estimators
Pot Estmato: defto of estmators Pot estmator: ay fucto W (X,..., X ) of a data sample. The exercse of pot estmato s to use partcular fuctos of the data order to estmate certa ukow populato parameters.
More informationTHE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 2
THE ROYAL STATISTICAL SOCIETY 06 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE The Socety s provdg these solutos to assst caddates preparg for the examatos 07. The solutos are teded as learg ads ad should
More informationClass 13,14 June 17, 19, 2015
Class 3,4 Jue 7, 9, 05 Pla for Class3,4:. Samplg dstrbuto of sample mea. The Cetral Lmt Theorem (CLT). Cofdece terval for ukow mea.. Samplg Dstrbuto for Sample mea. Methods used are based o CLT ( Cetral
More informationhp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations
HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several
More informationbest estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best
Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg
More informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationMultiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades
STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos
More informationOrdinary Least Squares Regression. Simple Regression. Algebra and Assumptions.
Ordary Least Squares egresso. Smple egresso. Algebra ad Assumptos. I ths part of the course we are gog to study a techque for aalysg the lear relatoshp betwee two varables Y ad X. We have pars of observatos
More information( ) = ( ) ( ) Chapter 13 Asymptotic Theory and Stochastic Regressors. Stochastic regressors model
Chapter 3 Asmptotc Theor ad Stochastc Regressors The ature of eplaator varable s assumed to be o-stochastc or fed repeated samples a regresso aalss Such a assumpto s approprate for those epermets whch
More information1 Solution to Problem 6.40
1 Soluto to Problem 6.40 (a We wll wrte T τ (X 1,...,X where the X s are..d. wth PDF f(x µ, σ 1 ( x µ σ g, σ where the locato parameter µ s ay real umber ad the scale parameter σ s > 0. Lettg Z X µ σ we
More informationChapter 4 Multiple Random Variables
Revew o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for Chapter 4-5 Notes: Although all deftos ad theorems troduced our lectures ad ths ote are mportat ad you should be famlar wth, but I put those
More informationLinear Regression with One Regressor
Lear Regresso wth Oe Regressor AIM QA.7. Expla how regresso aalyss ecoometrcs measures the relatoshp betwee depedet ad depedet varables. A regresso aalyss has the goal of measurg how chages oe varable,
More informationSTA302/1001-Fall 2008 Midterm Test October 21, 2008
STA3/-Fall 8 Mdterm Test October, 8 Last Name: Frst Name: Studet Number: Erolled (Crcle oe) STA3 STA INSTRUCTIONS Tme allowed: hour 45 mutes Ads allowed: A o-programmable calculator A table of values from
More informationRandom Variables. ECE 313 Probability with Engineering Applications Lecture 8 Professor Ravi K. Iyer University of Illinois
Radom Varables ECE 313 Probablty wth Egeerg Alcatos Lecture 8 Professor Rav K. Iyer Uversty of Illos Iyer - Lecture 8 ECE 313 Fall 013 Today s Tocs Revew o Radom Varables Cumulatve Dstrbuto Fucto (CDF
More informationCHAPTER 3 POSTERIOR DISTRIBUTIONS
CHAPTER 3 POSTERIOR DISTRIBUTIONS If scece caot measure the degree of probablt volved, so much the worse for scece. The practcal ma wll stck to hs apprecatve methods utl t does, or wll accept the results
More informationStatistics MINITAB - Lab 5
Statstcs 10010 MINITAB - Lab 5 PART I: The Correlato Coeffcet Qute ofte statstcs we are preseted wth data that suggests that a lear relatoshp exsts betwee two varables. For example the plot below s of
More information18.413: Error Correcting Codes Lab March 2, Lecture 8
18.413: Error Correctg Codes Lab March 2, 2004 Lecturer: Dael A. Spelma Lecture 8 8.1 Vector Spaces A set C {0, 1} s a vector space f for x all C ad y C, x + y C, where we take addto to be compoet wse
More informationModule 7: Probability and Statistics
Lecture 4: Goodess of ft tests. Itroducto Module 7: Probablty ad Statstcs I the prevous two lectures, the cocepts, steps ad applcatos of Hypotheses testg were dscussed. Hypotheses testg may be used to
More informationThe number of observed cases The number of parameters. ith case of the dichotomous dependent variable. the ith case of the jth parameter
LOGISTIC REGRESSION Notato Model Logstc regresso regresses a dchotomous depedet varable o a set of depedet varables. Several methods are mplemeted for selectg the depedet varables. The followg otato s
More informationModule 7. Lecture 7: Statistical parameter estimation
Lecture 7: Statstcal parameter estmato Parameter Estmato Methods of Parameter Estmato 1) Method of Matchg Pots ) Method of Momets 3) Mamum Lkelhood method Populato Parameter Sample Parameter Ubased estmato
More informationChapter 8. Inferences about More Than Two Population Central Values
Chapter 8. Ifereces about More Tha Two Populato Cetral Values Case tudy: Effect of Tmg of the Treatmet of Port-We tas wth Lasers ) To vestgate whether treatmet at a youg age would yeld better results tha
More informationMultiple Linear Regression Analysis
LINEA EGESSION ANALYSIS MODULE III Lecture - 4 Multple Lear egresso Aalyss Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Cofdece terval estmato The cofdece tervals multple
More informationEstimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
More informationå 1 13 Practice Final Examination Solutions - = CS109 Dec 5, 2018
Chrs Pech Fal Practce CS09 Dec 5, 08 Practce Fal Examato Solutos. Aswer: 4/5 8/7. There are multle ways to obta ths aswer; here are two: The frst commo method s to sum over all ossbltes for the rak of
More informationENGI 4421 Propagation of Error Page 8-01
ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.
More information6.867 Machine Learning
6.867 Mache Learg Problem set Due Frday, September 9, rectato Please address all questos ad commets about ths problem set to 6.867-staff@a.mt.edu. You do ot eed to use MATLAB for ths problem set though
More informationMultiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
More informationDr. Shalabh. Indian Institute of Technology Kanpur
Aalyss of Varace ad Desg of Expermets-I MODULE -I LECTURE - SOME RESULTS ON LINEAR ALGEBRA, MATRIX THEORY AND DISTRIBUTIONS Dr. Shalabh Departmet t of Mathematcs t ad Statstcs t t Ida Isttute of Techology
More informationMaximum Likelihood Estimation
Marquette Uverst Maxmum Lkelhood Estmato Dael B. Rowe, Ph.D. Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Coprght 08 b Marquette Uverst Maxmum Lkelhood Estmato We have bee sag that ~
More informationECON 5360 Class Notes GMM
ECON 560 Class Notes GMM Geeralzed Method of Momets (GMM) I beg by outlg the classcal method of momets techque (Fsher, 95) ad the proceed to geeralzed method of momets (Hase, 98).. radtoal Method of Momets
More informationObjectives of Multiple Regression
Obectves of Multple Regresso Establsh the lear equato that best predcts values of a depedet varable Y usg more tha oe eplaator varable from a large set of potetal predctors {,,... k }. Fd that subset of
More informationBIOREPS Problem Set #11 The Evolution of DNA Strands
BIOREPS Problem Set #11 The Evoluto of DNA Strads 1 Backgroud I the md 2000s, evolutoary bologsts studyg DNA mutato rates brds ad prmates dscovered somethg surprsg. There were a large umber of mutatos
More informationAnalysis of System Performance IN2072 Chapter 5 Analysis of Non Markov Systems
Char for Network Archtectures ad Servces Prof. Carle Departmet of Computer Scece U Müche Aalyss of System Performace IN2072 Chapter 5 Aalyss of No Markov Systems Dr. Alexader Kle Prof. Dr.-Ig. Georg Carle
More informationThe expected value of a sum of random variables,, is the sum of the expected values:
Sums of Radom Varables xpected Values ad Varaces of Sums ad Averages of Radom Varables The expected value of a sum of radom varables, say S, s the sum of the expected values: ( ) ( ) S Ths s always true
More informationMean is only appropriate for interval or ratio scales, not ordinal or nominal.
Mea Same as ordary average Sum all the data values ad dvde by the sample sze. x = ( x + x +... + x Usg summato otato, we wrte ths as x = x = x = = ) x Mea s oly approprate for terval or rato scales, ot
More informationTESTS BASED ON MAXIMUM LIKELIHOOD
ESE 5 Toy E. Smth. The Basc Example. TESTS BASED ON MAXIMUM LIKELIHOOD To llustrate the propertes of maxmum lkelhood estmates ad tests, we cosder the smplest possble case of estmatg the mea of the ormal
More informationRandom Variate Generation ENM 307 SIMULATION. Anadolu Üniversitesi, Endüstri Mühendisliği Bölümü. Yrd. Doç. Dr. Gürkan ÖZTÜRK.
adom Varate Geerato ENM 307 SIMULATION Aadolu Üverstes, Edüstr Mühedslğ Bölümü Yrd. Doç. Dr. Gürka ÖZTÜK 0 adom Varate Geerato adom varate geerato s about procedures for samplg from a varety of wdely-used
More informationParameter, Statistic and Random Samples
Parameter, Statstc ad Radom Samples A parameter s a umber that descrbes the populato. It s a fxed umber, but practce we do ot kow ts value. A statstc s a fucto of the sample data,.e., t s a quatty whose
More informationSTATISTICAL INFERENCE
(STATISTICS) STATISTICAL INFERENCE COMPLEMENTARY COURSE B.Sc. MATHEMATICS III SEMESTER ( Admsso) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITY P.O., MALAPPURAM, KERALA, INDIA -
More informationLogistic regression (continued)
STAT562 page 138 Logstc regresso (cotued) Suppose we ow cosder more complex models to descrbe the relatoshp betwee a categorcal respose varable (Y) that takes o two (2) possble outcomes ad a set of p explaatory
More informationf f... f 1 n n (ii) Median : It is the value of the middle-most observation(s).
CHAPTER STATISTICS Pots to Remember :. Facts or fgures, collected wth a defte pupose, are called Data.. Statstcs s the area of study dealg wth the collecto, presetato, aalyss ad terpretato of data.. The
More informationMidterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes
coometrcs, CON Sa Fracsco State Uversty Mchael Bar Sprg 5 Mdterm am, secto Soluto Thursday, February 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes eam.. No calculators of ay kd are allowed..
More informationChapter 9 Jordan Block Matrices
Chapter 9 Jorda Block atrces I ths chapter we wll solve the followg problem. Gve a lear operator T fd a bass R of F such that the matrx R (T) s as smple as possble. f course smple s a matter of taste.
More informationHomework 1: Solutions Sid Banerjee Problem 1: (Practice with Asymptotic Notation) ORIE 4520: Stochastics at Scale Fall 2015
Fall 05 Homework : Solutos Problem : (Practce wth Asymptotc Notato) A essetal requremet for uderstadg scalg behavor s comfort wth asymptotc (or bg-o ) otato. I ths problem, you wll prove some basc facts
More informationThe Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
More informationUnimodality Tests for Global Optimization of Single Variable Functions Using Statistical Methods
Malaysa Umodalty Joural Tests of Mathematcal for Global Optmzato Sceces (): of 05 Sgle - 5 Varable (007) Fuctos Usg Statstcal Methods Umodalty Tests for Global Optmzato of Sgle Varable Fuctos Usg Statstcal
More informationContinuous Distributions
7//3 Cotuous Dstrbutos Radom Varables of the Cotuous Type Desty Curve Percet Desty fucto, f (x) A smooth curve that ft the dstrbuto 3 4 5 6 7 8 9 Test scores Desty Curve Percet Probablty Desty Fucto, f
More informationTHE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 5
THE ROYAL STATISTICAL SOCIETY 06 EAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 5 The Socety s provdg these solutos to assst cadtes preparg for the examatos 07. The solutos are teded as learg ads ad should
More informationChapter 3 Sampling For Proportions and Percentages
Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys
More informationChapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements
Aoucemets No-Parametrc Desty Estmato Techques HW assged Most of ths lecture was o the blacboard. These sldes cover the same materal as preseted DHS Bometrcs CSE 90-a Lecture 7 CSE90a Fall 06 CSE90a Fall
More informationChapter 13 Student Lecture Notes 13-1
Chapter 3 Studet Lecture Notes 3- Basc Busess Statstcs (9 th Edto) Chapter 3 Smple Lear Regresso 4 Pretce-Hall, Ic. Chap 3- Chapter Topcs Types of Regresso Models Determg the Smple Lear Regresso Equato
More informationRecall MLR 5 Homskedasticity error u has the same variance given any values of the explanatory variables Var(u x1,...,xk) = 2 or E(UU ) = 2 I
Chapter 8 Heterosedastcty Recall MLR 5 Homsedastcty error u has the same varace gve ay values of the eplaatory varables Varu,..., = or EUU = I Suppose other GM assumptos hold but have heterosedastcty.
More informationLecture 8: Linear Regression
Lecture 8: Lear egresso May 4, GENOME 56, Sprg Goals Develop basc cocepts of lear regresso from a probablstc framework Estmatg parameters ad hypothess testg wth lear models Lear regresso Su I Lee, CSE
More informationA New Family of Transformations for Lifetime Data
Proceedgs of the World Cogress o Egeerg 4 Vol I, WCE 4, July - 4, 4, Lodo, U.K. A New Famly of Trasformatos for Lfetme Data Lakhaa Watthaacheewakul Abstract A famly of trasformatos s the oe of several
More informationESS Line Fitting
ESS 5 014 17. Le Fttg A very commo problem data aalyss s lookg for relatoshpetwee dfferet parameters ad fttg les or surfaces to data. The smplest example s fttg a straght le ad we wll dscuss that here
More informationLaw of Large Numbers
Toss a co tmes. Law of Large Numbers Suppose 0 f f th th toss came up H toss came up T s are Beroull radom varables wth p ½ ad E( ) ½. The proporto of heads s. Itutvely approaches ½ as. week 2 Markov s
More informationLecture Notes to Rice Chapter 5
ECON 430 Revsed Sept. 06 Lecture Notes to Rce Chapter 5 By H. Goldste. Chapter 5 gves a troducto to probablstc approxmato methods, but s suffcet for the eeds of a adequate study of ecoometrcs. The commo
More informationStatistics: Unlocking the Power of Data Lock 5
STAT 0 Dr. Kar Lock Morga Exam 2 Grades: I- Class Multple Regresso SECTIONS 9.2, 0., 0.2 Multple explaatory varables (0.) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (0.2) Exam 2 Re- grades Re-
More informationIntroduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
More informationChapter 13, Part A Analysis of Variance and Experimental Design. Introduction to Analysis of Variance. Introduction to Analysis of Variance
Chapter, Part A Aalyss of Varace ad Epermetal Desg Itroducto to Aalyss of Varace Aalyss of Varace: Testg for the Equalty of Populato Meas Multple Comparso Procedures Itroducto to Aalyss of Varace Aalyss
More informationAnalysis of Variance with Weibull Data
Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad
More informationM2S1 - EXERCISES 8: SOLUTIONS
MS - EXERCISES 8: SOLUTIONS. As X,..., X P ossoλ, a gve that T ˉX, the usg elemetary propertes of expectatos, we have E ft [T E fx [X λ λ, so that T s a ubase estmator of λ. T X X X Furthermore X X X From
More informationSTK3100 and STK4100 Autumn 2017
SK3 ad SK4 Autum 7 Geeralzed lear models Part III Covers the followg materal from chaters 4 ad 5: Sectos 4..5, 4.3.5, 4.3.6, 4.4., 4.4., ad 4.4.3 Sectos 5.., 5.., ad 5.5. Ørulf Borga Deartmet of Mathematcs
More informationLINEAR REGRESSION ANALYSIS
LINEAR REGRESSION ANALYSIS MODULE V Lecture - Correctg Model Iadequaces Through Trasformato ad Weghtg Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Aalytcal methods for
More informationTHE ROYAL STATISTICAL SOCIETY 2010 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 2 STATISTICAL INFERENCE
THE ROYAL STATISTICAL SOCIETY 00 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE STATISTICAL INFERENCE The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for the
More informationLecture 9: Tolerant Testing
Lecture 9: Tolerat Testg Dael Kae Scrbe: Sakeerth Rao Aprl 4, 07 Abstract I ths lecture we prove a quas lear lower boud o the umber of samples eeded to do tolerat testg for L dstace. Tolerat Testg We have
More information