. . Distribution function from Probability density function Both the probability density function and the cumulative distribution function (or distribution function) of a continuous random variable X contain all the probabilistic information of X . The probability distribution of X is determined by either of them.
Let us learn the method to determine the distribution function F of a continuous random variable X from the probability density function f x of X and vice versa. Example . If X is the random variable with probability density function f x given by, otherwise find (i) the distribution function F x (ii) P X ( . .
) (i) By definition F x f u du