Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0...

Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0 < p < 1. (a) (6pts) Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y = n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1

Solutions

Expert Solution

We are given here the distributions as:

a) The probability here is computed as:

This is the required probability here.

b) The probability here is computed as:

This is the required probability here.

Now the conditional probability here is computed as: (Using Bayes theorem)

This is the required probability here.

orchestra answered 1 year ago

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