Poisson Distribution

The probability mass function of the Poisson distribution is given by:

$$P(k;\lambda )=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$$

Binomial Distribution

The probability mass function of the binomial distribution is given by:

$$P(k;n,p)=(\genfrac{}{}{0ex}{}{n}{k})p^k(1-p{)}^{n-k}$$

Geometric Distribution

The probability mass function of the geometric distribution is given by:

$$P(k;p)=(1-p{)}^{k-1}p$$

Normal Distribution

The probability density function of the normal distribution is given by:

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

Exponential Distribution

The probability density function of the exponential distribution is given by:

$$f(x;\lambda )=\lambda e^{-\lambda x}\text{for }x\ge 0$$

Beta Distribution

The probability density function of the beta distribution is given by:

$$f(x;\alpha ,\beta )=\frac{x^{\alpha -1}(1-x{)}^{\beta -1}}{B(\alpha ,\beta )}\text{for }0<x<1$$

Gamma Distribution

The probability density function of the gamma distribution is given by:

$$f(x;\alpha ,\beta )=\frac{x^{\alpha -1}{e}^{-x/\beta }}{{\beta }^{\alpha }\mathrm{\Gamma }(\alpha )}\text{for }x\ge 0$$