STATS401HW7_Sol.pdf - HW7 Sol Stats 401 Instruction Team Question 1 Let U and V be iid(independent and identically distributed with mean \u00b5 and standard

# STATS401HW7_Sol.pdf - HW7 Sol Stats 401 Instruction Team...

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HW7 Sol Stats 401 Instruction Team February 16, 2019 Question 1LetUandVbe iid (independent and identically distributed) with meanμand standard deviationσ.a. What isV ar(14U+34V)? b. What isV ar(12U+2V)? c. Which has bigger variance? Question 2Consider the distribution with pmf given by:P(X=-1) = 0.4andP(X= 1) = 0.6. LetX1andX2beindependent and identically distributed random variables with this distribution.a. What isE(X1)andV ar(X2)? b. LetS=X1+X2, the sum ofX1andX2. What is the pmf ofS? (Determine first the possible valuesof S and then obtain the corresponding probabilities. This is the sampling distribution of c.LetY=S2=2. What is the distribution (that is, the pmf) ofY? (This is the sampling distributionof the sample mean based on two observations for this case.) 1
d.Compute E(Y) and Var(Y) and compare them to your answer in part (a). What relationship do youobserve? Question 3Recall the game in Question 3, Homework 6 (repeated briefly here: Joe Smith plays a betting game with hisfriends. He puts in one dollar to join the game. If he wins the game, he gets 2. If he loses, he gets nothing,so his gain is -1). Joe Smith is planning to play the game 100 times. The 100 outcomes will be independentof each other.a. What is his expected total gain if he plays 100 times?

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