Solution Found!
Use the result in Exercise 3.158 to prove that, if W = aY
Chapter 3, Problem 159E(choose chapter or problem)
Problem 159E
Use the result in Exercise 3.158 to prove that, if W = aY + b, then E(W ) = aE(Y ) + b and V (W ) = a2 V (Y ).
Reference
If Y is a random variable with moment-generating function m(t) and if W is given by W = aY + b, show that the moment-generating function of W is etbm(at).
Questions & Answers
QUESTION:
Problem 159E
Use the result in Exercise 3.158 to prove that, if W = aY + b, then E(W ) = aE(Y ) + b and V (W ) = a2 V (Y ).
Reference
If Y is a random variable with moment-generating function m(t) and if W is given by W = aY + b, show that the moment-generating function of W is etbm(at).
ANSWER:
Solution :
Step 1 of 1:
Let Y denotes a random variable with moment-generating function m(t).
Our goal is:
If W=aY+b. We need to prove that E(W)=aE(Y)+b and V(W)=.
Now we have to prove that E(W)=aE(Y)+b and V(W)=.
If W=aY+b we know that the moment generating function.