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.