Kiley Exam 2

# Kiley Exam 2 - Math 351 W.T Kiley Clearly show your work...

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Math 351 W.T. Kiley Clearly show your work and answers. Follow the Honor Code. \10) t X is normal with a mean of 10 and a variance of 25. Find: a) the probability that X is between 7 and 13; Exam2 December 2h 2009 b) an interval that has .92 probability of containing X. ^i ;r7;'?=l{) = r (-, 6 { z€' o) ='7 e 5 7-' A4743 = '' ?s/4 b), q ),= ?Fn < 2 4 0/,f .', .1 6 = PI As "7, ) -" /wt = /,75 .n, t[,zf= tX- to)/f ^. ( X ; /0t tr,7,f 07)Z Y is the mean of 36 independent values of the above X. Answer the same 2 questioas about Y. -"' E(f) = 10 ) Va+ 0)= ]Eb6 ; 7 = (r-rD/( %) ^)P0<Y<tz)= l:r,!,: z:,t,:) :n 7z6#{# l-) tl.zs: (ttd/tA-', /=/atl,qrg t, |O)t The p.d f of X is (*): lxl for -1 < x < 1. Find the p d.f. for: a) Y: X^3;b) Y:XnZ . ", f, d ?r; 6;1 t:#;{ r' / 4": } o R ry \$\ = F(x'r g) = \!,"' 1.il h ; I T l" {rtp - Fi ) Fytp = r(x Ar{,,il, F; tr) Z3 -7 \$)= le*l b ir-'" = qlr'llt ,ril;6t *Fn L= u't6 nt* It,2 S, t 8,1 5J ftr, s fi,il.1s|l i,hl/* -/ ,/,t, 0 ( 7 .l,

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11da X and Y are independent with p.d.f. f(t) = 0 1e"(-0 lt) for 0 < t S = X* Y Find: a) the joint p.d f. for (X,Y); b) the p.d.f. for S; c) the probability that 10 < X; d) the probability that l0 < d ( h,F={*H/rr7t --- - o,l o,ol * 4+fr= & 03a c\ rI) P0O1S) : / * f, fra) : /- (' n'' - i'" r) i tei' Y, /zo ,(ku)/z'1(,ot-d1>\ t: (,rl '/"1:
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