Probability density function of normal distribution

Normal distribution.

If X is random variable thenits normal distribution with parameters mean  m and variance σ2 is  given by 

\[f(x)=(\frac{1}{\sqrt{2\pi σ^2}})e ^{\frac{(x-m)^2}{2σ^2}}\]

where m is mean of random variable and σ^2 is variance of the random variable .

This function is bell shaped curve and that is symmetric about m

Boundary condition     x varies from -∞ to +∞.

For Normal distribution   Mean=E[X]=m

                                and Variance =V[X]=σ^2

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