Geometric Random Variable

Suppose X is a discrete random variable with range . X is called a geometric random variable if

            .

• X describes the outcomes of independent Bernoulli trials each with probability of success before a 'success' occurs. If the first success occurs at the trial, then the outputs of the Bernoulli trials are

•  is countably infinite, because we may have to wait infinitely long before the first success occurs.
• The geometric random variable with the parameter is denoted by