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Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose...

Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose that N is a random variable, independent of the Xi-s, that has a Poisson distribution with mean λ > 0. What is the expected value of X1 + X2 +···+ XN2?
(A) N2

(B) λ + λ2

(C) λ2

(D) 1/λ2

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