ELEC 321
# Three Important Distributions

Updated 2017-10-31

If random variable if and only if the PMF

The distribution function is just the sum of the PMF from 0 to the value of interest.

The corresponding **mean** and **variance** is:

Example: application of the uniform distribution include the noise generated from a quantizer

Exponential random variables has the distribution function

The PMF is the derivative.

The distribution takes one parameter , which is the rate of occurrence. .

The associated **mean** and **variance** can be calculated as follows.

The exponential random variables holds the the **memoryless property**: which states

If random variable follows a normal distribution, , its density function and distribution is as follows.