Handout #6

Date:

Distribution Functions for Continuous Random Variables (CRVs)

The distribution function for discrete random variables (DRVs) is:

F( x ) = P ( X � x ) = S f ( u ), for all u � x.

(We've seen this before.)

The distribution function F( x ) for a CRV is defined by:

At the points of continuity of f(x), the � function can be replaced by < if desired.

Example.

The probability that X is between x and x + D x is given by:

As Dx � 0,

Taking the derivative of both sides,

everywhere where f(x) is continuous, so that the derivative of the distribution function is the density function.