Q.Define probability density function for normal variable.

In the normal p.d.f. the constants used are $\pi \approx 3.1416$ and $e \approx 2.7183$.

Explanation. The probability density function of a normal variable is

$f(x)=\frac{1}{\sigma\sqrt{2\pi}}\,e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},\qquad -\infty<x<\infty.$ …

$f(x) = \dfrac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ for $-\infty < x < \infty$.

A continuous random variable $X$ is said to follow a normal distribution with parameters mean $\mu$ and standard deviation $\sigma$ ($\sigma > 0$) if its probability density function is

$f(x) = \frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x-\mu)^2}{2\sigma^2}}, \qquad -\infty < x < \infty$

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