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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?
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'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
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_\ 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(ZX)] 2 E(Z)? Is Var(E[ZX]) 2 Var(Z)? ...
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 Spring '07
 SHIM

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