Let Z = X + Y. 1. Find the expectation E[Z]. E[Z] = 8.1667
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How was the correct answer of 8.1667 attained?
![Suppose the joint PMF of the random variables X and Y is
P(X= x, Y = y)
Let Z = X + Y.
1. Find the expectation E[Z].
E[Z]=8.1667
=
x+y
72
if(x, y) {5,6,7} × {1, 2, 3},
0 Otherwise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1467f162-7185-45ab-925a-2589d3c8cce7%2F25c0d578-dd85-443e-985d-cf75ee0b3ac4%2Fe3w95hz_processed.png&w=3840&q=75)
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- Find E(R) and V (R) for a random variable R whose moment-generating function ismR(t) = e2t(1-3t2)-1Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?Use the moment generating function to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n.Find the distribution of Y = X1 + · · · + Xn.
