The following is the plot of the normal probability density function. Cumulative Distribution Function The cumulative distribution function (cdf) is the probability that the variable takes a value less than or equal to x. That is \( F(x) = Pr[X \le x] = \alpha \) For a continuous distribution, this can be expressed mathematically as \( F(x) = \int_{-\infty}^{x} {f(\mu) d\mu} \) For a discrete distribution, the cdf can be expressed as \( F(x) = \sum_{i=0}^{x} {f(i)} \) The following is the plot of the normal cumulative distribution function. The horizontal axis is the allowable domain for the given probability function. Since the vertical axis is a probability, it must fall between zero and one.