\[ P(X = n) = (1 - p)^{n} \]
Expected number of failures before success
\[ E(X) = \frac{1-p}{p} \]
\[ \sigma^{2} (X) = \frac{1 - p}{p^{2}} \]
\[ P(X = n) = \frac{\lambda^{n}}{n!} e^{- \lambda} \]
Expected value is just going to be the rate, which is \(\lambda\)
\[ E(X) = \sigma^{2} (X) = \lambda \]
\[ f(t; \mu ) = \mu e^{- \mu t} \]
Where:
Probability of time \(t\) elapsing between successive independent events
\[ E(X) = \frac{1}{\lambda} \]
\[ \sigma^{2} (X) = \frac{1}{\lambda^{2}} \]
\[ C_{x} = \text{coefficient of variance} = 1 \]
Collection of random variables