Math Formulas || Probability || Distribution

$P(x)=\dfrac{1}{\sqrt{2\pi \sigma^{2}}}\;e^{-\dfrac{(x-\mu)^{2}}{2\sigma^{2}}}$

Where,

$\mu$ = Mean

$\sigma$ = Standard Distribution

$\sigma^2$ = Variance

$x$ = Normal random variable

If mean ($\mu$) = 0 and standard deviation ($\sigma$) = 1, then this distribution is known to be normal distribution.

$P(x)$ $=~ \dfrac{n!}{r!(n-r)!}\cdot p^{r}(1-p)^{n}$ $=~ C(n, r)\cdot p^{r}(1-p)^{n-r}$

Where,

$n$ = Total number of events

$r$ = Total number of successful events

$p$ = Probability of success on a single trial

$1 - p$ = Probability of failure

$P(x)=\dfrac{\lambda^{x}}{x!}~e^{-\lambda}\:$

Where,

$\lambda$ is the average number

$x$ is a Poisson random variable

$e$ is the base of logarithm

$P(x)={\lambda^{x}}~e^{-\lambda}\:$

Where,

Mean = $\lambda^{-1}$

Variance = $\lambda^{-2}$