solutionsexam1a

solutionsexam1a - 1 Rolling die Suppose that you...

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Unformatted text preview: 1 Rolling die Suppose that you continually roll a die until the sum of all the rolls exceeds 100 (then you stop). What is the most likely value of this total when you stop? Coult'lm‘. an W VO/W a: (we 9”“ PM»; (0 QKCEQ&t% ilk 2 Samples and Correlation Assume that the correlation between X and Y is .5. X, has this distribution: a Elﬁn“ Y, has this distribution a “man What is the probability that the sample mean for X is greater than the sample mean for Y? '5 \ \_ () {in EMA/40‘) 4) ><=J %; e, we, ~ =(( ~ ~ \$43 #1709 YAMCecX),V—‘§i’) V V) w \7AW637),Wi/’T’) éy W («C-7‘. "‘ * :9???) eA/(KRI) ‘ , Z> x V C I 7 M Adv [wee—s?) V2 31 Veil? ‘37): Vere?) xix/«7) tQQK/z/V { (2% (K7?) ~> evafxnizﬂ: {1 Mgr/33g? =4; 12% =49 ﬂew-i ~7 This page intentionally left blank / (\ .‘ ’13 09,»: ‘3'“ WW“ '1 l ( (KM) 109W!) 3 Let X ~ Poi(/\) What is 1P({Waittime forX = k} S t)? What is E({Waz't time forX = What is Var({VVait time forX = What is fox 1P({Wait time for X = k} > t)dt Q6 4 Transformation Question Let Y = ex. Find the pdf of Y if X ~ U(0, 1). What is E(Y) and Var(Y). t) CK: §’{/§\{G[/,e]j ' ~— 2 *1 H) " 7 a > VqCY): 5(7)) {56/17: " (VB 5 9 Q # ~: {M 40 ff: @0/ _\ S\/6 6424 ll 5 Short (er) Answers o Let X ~ N(5, 16). What is 19(1 3 X s 9)? What is IP’(—3 g X g 13)?. What is M5 3 X g 17)?. 0 Suppose (X, Y) ~ N2((px,py).ag,a§,p). What is the expected value of X, when Y = 17 0 Suppose Z = X + Y. Is E[E(Z|X)] 2 E(Z)? Is Var(E[Z|X]) 2 Var(Z)? ...
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This note was uploaded on 11/08/2009 for the course ISYE 2028 taught by Professor Shim during the Spring '07 term at Georgia Tech.

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solutionsexam1a - 1 Rolling die Suppose that you...

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