Suppose §1, $2, ... are iid random variables having mean u and variance o?. Form the random sum SN = E1 + · ·. (a) Derive the mean and variance of SN when N has a Poisson distribution with parameter d. (b) Determine the mean and variance of SN where N has a geometric distributions with mean 1 = -2. (c) Compare the behaviors in (a) and (b) as A→ 0.

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A:

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A: Solution

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A: The mean is calculated as follows:

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