4.20. How can I show that X is a Poisson random variable with parameter lambda, then E[Xn] =.... ? And after, using this result to compute E[X3]?

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4.20. How can I show that X is a Poisson random variable with parameter lambda, then E[Xn] =.... ? And after, using this result to compute E[X3]?

1. What value
maximizes P{X = k}, k ≥ 0?
4.20. Show that X is a Poisson random variable with parameter 1, then
E[X"] = AE[(X + 1)-1]
Now use this result to compute E[X³].
4.21. Consider n coins, each of which independently comes up heads with
Suppo
that n is large and n is small and let 2 nn Sunnd
hobility
Transcribed Image Text:1. What value maximizes P{X = k}, k ≥ 0? 4.20. Show that X is a Poisson random variable with parameter 1, then E[X"] = AE[(X + 1)-1] Now use this result to compute E[X³]. 4.21. Consider n coins, each of which independently comes up heads with Suppo that n is large and n is small and let 2 nn Sunnd hobility
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