ELEC 321

Three Important Distributions

Updated 2017-10-31

Uniform

If random variable $X\sim\text{Uniform}(a, b)$ 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

Exponential random variables has the distribution function

The PMF is the derivative.

The distribution takes one parameter $\lambda$, which is the rate of occurrence. $\lambda >0$.

The associated mean and variance can be calculated as follows.

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

Gaussian / Normal

If random variable $X$ follows a normal distribution, $X\sim\text{N}(\mu, \sigma^2)$, its density function and distribution is as follows.