A random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X is a uniform(0,1) random variable. What is E[Y]?
E[Y] = np
The Attempt at a Solution
The key is determining the probability of success, which is stated as X, thus the answer should be nX. But X is a uniform(0,1) random value, which is what I find confusing. My first thought was that X is constant = 1 (because uniform distribution) and therefore E[Y] = nX = n but I don't think that's right (it's like a double headed coin, n flips = n successes). I guess I don't understand how the fact that X is a uniform(0,1) RV enters into the problem. Any hints?