Conditional expectation. 5. Suppose (Zk) are iid N(0, 1) and suppose N is an independent Poisson (1) random variable. Compute using the law of total expectation 4 N ΕΙΣ ΖΗ k=1 Hint: the law of the sum of k independent N(0, 1) random variables is N (0, k).
Conditional expectation. 5. Suppose (Zk) are iid N(0, 1) and suppose N is an independent Poisson (1) random variable. Compute using the law of total expectation 4 N ΕΙΣ ΖΗ k=1 Hint: the law of the sum of k independent N(0, 1) random variables is N (0, k).
A First Course in Probability (10th Edition)
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Transcribed Image Text:Conditional expectation.
5. Suppose (Zk) are iid N(0, 1) and suppose N is an independent Poisson (1)
random variable. Compute using the law of total expectation
E
N
Σ Z k
k=1
4
Zk) ₁
Hint: the law of the sum of k independent N(0, 1) random variables is
N (0, k).
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