±*={4. ! --t x > 2. =fifhdt=f tdt. k 51 : III (24-04)=1. Sf pandx. Soak x' dx XLO. Math 128 Exam 2 Review Questions

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1 Math 18 Eam Review Questions E 1) Given p() k 3 where 0 Find the value of k that would make this function a PDF (A) 3 8 (B) 1 4 (C) (D) 5 8 ) Given the following PDF: Sf pand Soak d k 51 : (404)1 ffhdtf tdt 0 t < 0 ±*{4 t f(t) 0 t { 0 t > 4k lk! t > XL H s Find it s CDF (A) 1 (B) 4 (C) (D) 1 4

2 3) Calculate the mean for the PDF given below: So PH fi ) (A) 3 4 (B) 1 4 (C) 3 tu f * * pcid 0 < 0 f() { 0 > 1 to S N Xfiid Sos d Z to Eli o ) (D) 1 4) Given the following PDF, calculate the mean Phil MX to M X t 15 µfpiid ma# o So So 1 lpcstoxt 5 ttsottstd Fo t tsd f o HM to tooth P (A) 50 (B) 33 (C) 5 (D) 38 5) Calculate the median in the PDF given in #4 (A) 75 (B) 9 (C) 38 (D) 33 E Sotpild o+ysd t PDF Fo 10 c t Et! too too # orint#tzofiin:tidn::::fhoi:?qer T than 10

3 S, Fo ttsd Fo f t i Foot f s) ( foot 45 ) 6) Using the PDF given in #4, calculate P(1 4) (A) 11 0 (B) 15 0 (C) 13 0 (D) 9 7) Suppose we wait for a bus each morning Let t represent the waiting time until the bus arrives each day f we assume t is eponentially distributed with an average wait time of 8 minutes, then which of the following is the PDF for this model (A) e 015t (C) e015t (D) 1 e 015t 8) Using the scenario given in question #7, what is the median for this distribution? (A) 80 (B) 015 (C) 555 (D) 683 9) Which of the following is the CDF for the distribution given in #7? (A) 1 e 015t must we have g) 1030 (B) e 015t + 1 (C) 015te 015t (D) e 015t PCH 10) Suppose give an eam with normally distributed scores f the mean of the eams is a 65 and the standard deviation is a 15, then calculate P(55 X 80) (A) 009 (B) 066 (C) 016 (D) ) Using the same distribution as given in question 10, what is the probability of a randomly chosen person receiving between a 70% and an 80% on the eam? (A) 03 (B) 01 (C) 058 (D) 03 fi#e4efdossgshfo9earei EEd t foe Foo offemse µ H (B) 015e 015t T or X 4g 15 4,58 F 84 1 a 5545 Cii) 1in H ) + a and o E CH µ to

4 1) Using the same distribution as question 10, which of the following represents P(35 65)? From 10, µ 65 and 615 (A) p(65) p(35) 65 ( 65) 65 1 (B) 15 π e (15) d P ) S paddy ( 65) 65 1 (C) 15 π e (15) dμ 35 8 (D) d ( 65) [ 1 d 15 π e (15) ]! t e d an is the CDF 13) Given a PDF of p() e on 0 <, which of the following is the CDF? (A) 1 e (B) 1 + e (C) 1 e + e (D) 1 e e methodic : compute N f methods : Recall m 14) f p() is a pdf and F() it it s CDF, then which of the following is true? pltldt directly pan XEX, so it Cay not be A or B did, (c) ± pan, but +1D) p H CDo This! ) (A) p () F() (B) p() F(t)dt 0 (C) F () p() (D) None of these EH pftldt is the CDF EmP 15) f F() is a CDF and it s pdf is p(), then the mean μ is given by the following: (A) p()d (B) p()d just the definition (C) p(μ) 1 (D) F() tp(t)dt

5 16) f p() is a pdf on the interval 1 5, given in the graph below: P fit an 11pA dt an %,s X > 5 k i p() dt Ftl, 1 5 th D Then, it s CDF is: (A) 1 ( 1) (B) 5( 1) (C) 4( 1) (D) 1 ( 1) ) f f(, y) ln(y), find f (, y) (A) 1 + ln(y) (B) 1 y ln(y) + 1 (C) ln(y) + y (D) y ln(y) + C n f th ( n Ky ) ) t ftpcyl) nky t ftpytlnlyl Profit n Hy ) ( )

6 f (, ye D M y 18) Calculate f for f(, y) ye y (A) ye y t EY ( y yaey e Y y ) Yk D Ye ( oy to, ) (B) y e y (C) y 3 e y (D) 3 e y j 19) Find the critical value for f(, y) 3 + y + y 1 (A) (3,1) (B) (3, 3) (C) ( 3,3) (D)(3,3) 0) Find f of f(, y) 3 9 y y 3 1(A) 3 18y y 3 f 3 (B) 9 6y (C) 3 18 ffftcyehyyehtetlykyyeyteco (D) 3 + y y 3 sinlioyylltkoycosfloy 1) Find f y of f(, y) ( 3 y 3 8) (A)1 y 3 ( 3 y 3 8) (B) ( 3 y 3 8) (C) (6 y 3 ) (D) 1 3 y ( 3 y 3 8) ) Find f of f(, y) sin (10y y) (A) sin(10y y) cos(10y y) 6 (B) 0y sin(10y y) cos(10y y) (C) sin(10y y)(0y 1) (D) (40y ) sin(10y y) cos(10y y) l8y y Chainthslefy set)y ( l y ( 3/8) 1578%( 338) y (6 310) 913y(Bf8) C sin ( to yay ) f ( d y)

7 _ F K t D ytjththcytgytt#jh ) they if,, 3) Find f of f(, y) ln(y ) o (A) y (y ) y (B) (y ) 4) Find f y of f(, y) + y e +y (A) e +y (B) e +y (C) e +y (D) y e+y (C) (D) y (y ) F f y (y ) 5) Find a critical value for the following function: f(, y) + y + y 3 + (A) (,1) (B) (1, 1 ) (C) (0,0) (D) (, 1) e i ety H net page 6) Find the critical value(s) for the following function: f(, y) 3 + y 3 9y (A) (0,0), (3,3) (B) (3,3) (C) (1,1) (D) ( 3, 3) net pase 6 7) #EMAkESENSE Find f (, y) 7 y 4 (A) y 4 7 (B) 6 y 4 6 (C) y 4 (D) y ( 7 y 4 ) 5 y 4 8) Find a critical value for f(, y) ye + y 1 (A) (0,0) (B) ( 1, e ) (C) (, e 9) Find the critical values f(, y) 1 + y 1 ) (D) ( 1, e1 ) (A) ( 1,1) (B) (1,1) (C) ( 1,1), (1,1) (D) No critical values work it out! ty y Epose

8 5L : f, ty 30 y 3 X Fy Xtyo Xt : F 3 9,10 Fy 3yE9 o G 30 c *f (57)0 443 T4 S X 4350 or X 77 3! T Ye tµ y 9 and plug into f i Etc To Eat E aeto and y ety