4.4 Binomial distribution  (Page 3/3)

A discrete random variable (RV) which arises from Bernoulli trials. There are a fixed number, n , of independent trials. “Independent” means that the result of any trial (for example, trial 1) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X ~ B ( n , p ) . The mean is μ np and the standard deviation is σ = npq . The probability of exactly x successes in n trials is P ( X = x ) = n x p x q n − x .