100%(2)2 out of 2 people found this document helpful
This preview shows page 1 - 3 out of 7 pages.
HW7 SolStats 401 Instruction TeamFebruary 16, 2019Question 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 ofc.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?