I am given n independent Bernoulli trials, prob success = p. If X is # of successes, and Y is the number of failures, what is E(XY) and Cov(X,Y)? I was trying to use E(XY) - E(X)E(Y), the second component is easy, but I can't think of an easy way of finding E(XY) (maybe there isn't any?) Thanks!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The number of successes and failures have to add up to $n$, i.e. $X+Y=n$, so you can write
$$E[XY] = E[X(n-X)] = E[nX - X^2] = nE[X] - E[X^2]$$
Does that help?