ENGI 4421 Probability & Statistics
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1 Lecture Ntes fr ENGI 441 Prbablty & Statstcs by Dr. G.H. Gerge Asscate Prfessr, Faculty f Engneerng and Appled Scence Seventh Edtn, reprnted 018 Sprng
2 Table f Cntents 1. Descrptve Statstcs. Intrductn t Prbablty 3. Cuntng Technques 4. Laws f Prbablty; Bayes Therem 5. Dscrete Randm Quanttes; Expected Value and Varance 6. Cntnuus Randm Quanttes 7. Lnear Cmbnatns f Randm Quanttes; Jnt Prbablty Dstrbutns; Crrelatn; Pnt Estmatn; Bas and Precsn 8. Prpagatn f Errr 9. Dscrete Prbablty Dstrbutns 10. Cntnuus Prbablty Dstrbutns 11. Central Lmt Therem; One-sample Cnfdence Intervals 1. Tw-sample Cnfdence Intervals 13. Hypthess Tests 14. Ch-Square Tests 15. Smple Lnear Regressn Appendces: 16. Suggestns fr Frmula Sheets 17. Statstcal Tables
3 Lst f Symbls: prper subset subset,, ntersectn (same as lgcal AND), unn = lgcal nclusve OR Ø empty set = null set = {} prbablty f type I errr b x; n, p bnmal p.m.f. B x; n, p bnmal c.d.f. 1 prbablty f type II errr prbablty f type II errr f 0 ˆ 1 ntercept f regressn lne 0 estmate f 0 1 ˆ slpe f regressn lne 1 estmate f 1 CI cnfdence nterval c bundary f rejectn regn r CI (ne-sded) c L lwer bundary f tw-sded rejectn regn r CI c U upper bundary f tw-sded rejectn regn r CI n C r number f cmbnatns f r bjects frm n Cv XY, cvarance ch-square dstrbutn wth degrees f freedm, c fr whch P c E an event (value 1 f true, else 0) c * E r ~E r nt-e r E r E r E r E the cmplement f event E E X expected value f X e e resdual fr th pnt (n SLR) r number expected n cell f the null hypthess s true ( tests) e j number expected n cell (, j) f the null hypthess s true f f true errr fr th pnt (n SLR) value f F statstc = MSR/MSE frequency (number f bservatns n th nterval) x prbablty densty functn (pdf) f Fx cumulatve dstrbutn functn (cdf) PX x x gamma functn (= (x 1)!) r, gamma dstrbutn H null hypthess H A r H a r H 1 alternatve hypthess IQR nterquartle range ccurrence rate (n Pssn and expnental dstrbutns) x sample medan ppulatn medan MAD mean abslute devatn frm the mean MSE mean square errr s MSR mean square regressn X sample mean (estmatr) x sample mean (estmate) ppulatn mean * psterr estmate f (Bayesan) prr estmate f (Bayesan) r value f f null hypthess true n sample sze N ppulatn sze N, nrmal dstrbutn wth mean, varance number f degrees f freedm number bserved n cell
4 Lst f Symbls (cntnued) j number bserved n cell (, j) j number bserved n rw number bserved n clumn j ttal number bserved = n p ppulatn prprtn p E prbablty that event E P ccurs P A B cndtnal prbablty (that event A ccurs gven that event B has ccurred) p x P X x prbablty mass functn (pmf) fr dscrete x px, y P X x Y y p x p x, y margnal pmf X y py X y x p x, y px x P ˆp sample prprtn (estmatr) sample prprtn (estmate) * p adjusted ˆp (Agrest-Cull CI) n P r number f permutatns f r bjects frm n PI predctn nterval (SLR) z standard nrmal p.d.f. z standard nrmal c.d.f. q p 1 p cmplement f the prbablty p Q1 P cmplement f P qˆ1 pˆ cmplement f ˆp q L r x L lwer quartle q U r x U upper quartle * q adjusted ˆq (Agrest-Cull CI) r sample crrelatn r p r dds that an event wth 1 p prbablty p ccurs. r f / n relatve frequency ppulatn crrelatn S sample space = unversal set = pssblty space (set f all pssble utcmes) s sample standard devatn s sample varance ppulatn standard devatn ppulatn varance prr varance (Bayesan) * psterr estmate f (Bayesan) Sxy n xy x y Sxx n x x S n y y yy SIQR sem-nterquartle range SLR smple lnear regressn s.e. standard errr / n SSE sum f squares due t errr SSR sum f squares due t regressn SST ttal sum f squares T randm quantty fllwng t - dstrbutn wth degrees f freedm t, t fr whch P T t t bserved value f t bs V X varance f X w w d ŷ Z prr weght (Bayesan) data weght (Bayesan) value f y predcted frm regressn lne standard nrmal randm quantty P Z z z z fr whch z bs bserved value f z v
5 v
6 ENGI 441 Curse Outlne Page 0-01 [Replace ths sheet by the Curse Outlne handut that s suppled durng the frst week f classes n ths curse]
7 ENGI 441 Curse Outlne Page 0-0 [Replace ths sheet by the Curse Outlne handut that s suppled durng the frst week f classes n ths curse]
8 ENGI 441 Curse Outlne Page 0-03 [Replace ths sheet by the Curse Outlne handut that s suppled durng the frst week f classes n ths curse]
9 ENGI 441 Curse Outlne Page 0-04 [Replace ths sheet by the Curse Outlne handut that s suppled durng the frst week f classes n ths curse]
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