### Math 225 Course Notes

### Section 4.5: Continuous Probability Distributions

The distribution of a continuous random variable is described by a
probability density function,
a curve that does not go below the horizontal axis
for which the total area below the curve equals one.

Any curve f(x) that never dips below the horizontal axis
and for which the total area under the curve and above the axis is one,
describes the distribution of a continuous random variable.
The probability that the random variable falls in between the values
a and b is the area under the curve between a and b.
In probability notation,
this fact is expressed as
P(a < X < b) = Area under f(x) between a and b.

In more advanced treatments,
calculus may be used to find these areas.
All of the probability density functions that we will be using this semester
have their cumulative distributions tabulated in the back of the book.

Last modified: Feb 5, 1996

Bret Larget,
larget@mathcs.duq.edu