Question: 3.5. Let X(t) be a Poisson process with parameter A. Independently, let T be a random variable with the exponential density fT(t) = Oe for

3.5. Let X(t) be a Poisson process with parameter A. Independently, let T be a random variable with the exponential density fT(t) = Oe for t > 0.

Determine the probability mass function for X(T).

Hint: Use the law of total probability and I, (6.4). Alternatively, use the results of I, Section 5.2.

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