## Normal Distribution

A continuous random variable $X$ is said to have a normal distribution if its probability density function is given by $$\begin{equation*} f(x;\mu, \sigma^2) = \left\{ \begin{array}{ll} \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2\sigma^2}(x-\mu)^2}, & \hbox{-\infty< x<\infty, -\infty<\mu<\infty, \sigma^2>0;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*}$$ where $\mu$ and $\sigma^2$ are the parameters of normal distribution. In notation it can be written as $X\sim N(\mu, \sigma^2)$.

## Mean Normal distribution

The mean of normal distribution is

## Variance of Normal distribution

Variance of normal distribution is

## Mode of Normal distribution

The mode of normal distribution is

## Median of Normal distribution

The median of normal distribution is

## M.G.F. of Normal Distribution

The m.g.f. of $N(\mu,\sigma^2)$ distribution is

## Mean deviation about mean

The mean deviation about mean is