Question: A random variable, W, has first two moments given as follows: E [W] = 3 hours and E [W2 ] = 10.5 Consider a Poisson

A random variable, W, has first two moments given as follows: E [W] = 3 hours and E [W2 ] = 10.5 Consider a Poisson process, N = {N(t) : t ≥ 0}, such its first arrival time has E [S1] = 7.5 minutes. Assume that the process does not depend on W. Introduce a random variable, Y, such that Y = N(W).

1. Find the expected value of Y

2. Determine variance of Y

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