Need help with these probability questions 1 Suppose the ran

Need help with these probability questions.

1.) Suppose the random variable X ~Pois(lambda). Find E(1/(1+X)).

2.) Suppose the random variable X~Gamma(alpha, 1). Find E(X^3).

Solution

a) P{x<2} = P((X-mean)/s <(2-20)/4)

=P(Z<-4.5) =0 (from standard noraml table)

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b) P{6<x<12} = P((6-20)/4 <Z< (12-20)/4)

=P(-3.5<Z<-2) = 0.0225 (from standard noraml table)