8.3 Confidence interval for a population proportion (modified r.

A discrete random variable (RV) which arises from the Bernoulli trials with the next additional requirements. There are fixed number, n, of independent trials. “Independent” means that the result to any trial (for example, trial 1) in no way affects the answer to all 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 success in n trials. The notation is: X ~ B ( n , p ) ; the domain is the mean is μ np , and the variance is σ 2 = df . The probability to have exactly x successes in n trials is P ( X = x ) = n x p x q n − x .