Question

Let t be a random value of a variable with exponential density e −t , t > 0, and let Y be Poisson with parameter t. Find P(Y = 2).

A. 1/4

B. 1/2

C. 1/8

D. 1/e

Answer 1

We are given here that:

Where the distribution of T is given here as:

The probability here is computed using the law of total probability as:

Using the product rule here, we have here:

If we continue this we, we get the final expression here as:

Using the sum of an infinite geometric progression, we get here:

Therefore 1/2 = 0.5 is the required probability here.