# Binomial + Condition Distribution

1. Jul 23, 2009

### cse63146

1. The problem statement, all variables and given/known data

Let X be a binomial random variable representing the number of successes in n independent Bernoulli trials. Let Y be the number of successes in the first m trials, where m < n . Find the conditional probability distribution of Y given X=x.
2. Relevant equations

3. The attempt at a solution

So I think I need to use $$f_{Y|X} (Y|X) = \frac{f(x,y)}{f_X (X)}$$

where f(x,y) = n-mCxpxqn-m-x + mCypyqm

am I correct?