4. We are given two independent random variables X & Y that define a new one W=X+Y. The first RV Y has the moment generating function (MGF) oy (s) = 1/(1-s). The second RV X has the moment generating function x (s) = 1/(1-s)4 a. What are E[Y], E [Y²] and E[Y³] b. What is E[W²] Hint: Consider the examples in Chp 9 on sum of two variable and the Table given for the MGFs.

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4. We are given two independent random variables X & Y that define a new one W=X+Y. The first RV Y
has the moment generating function (MGF) þy(s) = 1/(1 - s). The second RV X has the moment
generating function x(s) = 1/(1 — s) 4
a. What are E[Y], E [Y²] and E[Y³]
b. What is E[W²]
Hint: Consider the examples in Chp 9 on sum of two variable and the Table given for the MGFs.
Transcribed Image Text:4. We are given two independent random variables X & Y that define a new one W=X+Y. The first RV Y has the moment generating function (MGF) þy(s) = 1/(1 - s). The second RV X has the moment generating function x(s) = 1/(1 — s) 4 a. What are E[Y], E [Y²] and E[Y³] b. What is E[W²] Hint: Consider the examples in Chp 9 on sum of two variable and the Table given for the MGFs.
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