Salohcin

07-26-2010, 01:31 PM

Hello all.

I am having a bit of confusion taking the conditional expectation of a binomial cumulative distribution. Lets say the probability of a success is x, and the probability of a failure is 1-x. We have n trials.

What is the expected number of successes given that less than k of our n trials ended in a success? Let me give an example for exposition. We flip a fair coin ten times, what is the expected number of heads given that less than 3 heads were flipped?

I suspect the answer is quite straightforward. Any help would be appreciated (I would particularly like a link to a nice website that explains conditional binomial distributions if anybody knows one off hand).

Thanks very much for the help,

Sincerely,

Nick

I am having a bit of confusion taking the conditional expectation of a binomial cumulative distribution. Lets say the probability of a success is x, and the probability of a failure is 1-x. We have n trials.

What is the expected number of successes given that less than k of our n trials ended in a success? Let me give an example for exposition. We flip a fair coin ten times, what is the expected number of heads given that less than 3 heads were flipped?

I suspect the answer is quite straightforward. Any help would be appreciated (I would particularly like a link to a nice website that explains conditional binomial distributions if anybody knows one off hand).

Thanks very much for the help,

Sincerely,

Nick