11.5. Summary#
Below is a summary table of the four previously discussed common probability distributions.
Name |
PMF or PDF |
Mean |
Variance |
Type |
Parameter(s) |
|---|---|---|---|---|---|
\(\begin{cases} p & x=1\\ 1-p & x=0 \end{cases}\) |
\(\sum_x x p(x)\) |
\(\sigma_X^2 = \sum_x (x - \mu)^2 p(x)\) |
Discrete |
\(p\) |
|
\(\begin{cases} \frac{n!}{x!(n-x)!} p^x (1-p)^{n-x} & x=0,1,...,n\\ 0 & \mathrm{otherwise} \end{cases}\) |
\(n p\) |
\((1-p)\) |
Discrete |
\(p\), \(n\), \(x\) |
|
\(\begin{cases} e^{-\lambda} \frac{\lambda^x}{x!} & \text{if } x \text{ is a non-negative integer} \\ 0 & \mathrm{otherwise} \end{cases}\) |
\(\lambda\) |
\(\lambda\) |
Discrete |
\(\lambda\) |
|
\(f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-(x-\mu)^2 / (2\sigma^2)}\) |
\(\mu\) |
\(\sigma^2\) |
Continuous |
\(\mu\), \(\sigma\) |