Name Form PDF CDF $E[X]$ $Var[X]$ Uniform $(a, b)$ $% $ $% b \\ \end{cases} %]]>$ $\frac{b+a}{2}$ $\frac{(b-a)^2}{12}$ Exponential $(\lambda)$ $% $ $% $ $\frac{1}{\lambda}$ $\frac{1}{\lambda^2}$ Erlang $(n, \lambda)$ $% 0 \\ 0 & \text{otherwise} \\ \end{cases} %]]>$ $\frac{n}{\lambda}$ $\frac{n}{\lambda^2}$ Gaussian $(\mu, \sigma)$ $\frac{1}{\sigma\sqrt{2\pi}}e^{-(x-\mu)^2/2\sigma^2}$ *$\Phi(z) = \frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^z e^{-u^2/2} du$ $\mu$ $\sigma^2$
• * Note that this is the standard normal CDF of the Gaussian random variable. To adjust for $\mu$ and $\sigma$ use $\Phi(\frac{x - \mu}{\sigma})$