Question: 5.3.5 Let X.t/ be a Poisson process with parameter . Independently, let T be a random variable with the exponential density Determine the probability mass

5.3.5 Let X.t/ be a Poisson process with parameter . Independently, let T be a random variable with the exponential density

Determine the probability mass function for X.T/.
Hint: Use the law of total probability and Chapter 1, (1.54). Alternatively, use the results of Chapter 1, Section 1.5.2.

fr(t)=0e-t fort > 0.

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