Consider an experiment for which there are two possible results: success if some event occurs, or failure if the event does not occur. If we repeat this experiment in a number of independent trials, we call it a binomial experiment. The probability of a success p must be constant for all trials. Since success and failure are complementary events, the probability of a failure is 1- p and is constant for all trials. The random variable Xis the total number of successes inn trials.
Binomial Distribution :
For a Binomial Distribution of n trials with the probability p of success on each trial, the mean (expectation) of the number of successes is:
µ = E(x) = np