Expectation of Erlang Distribution
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Theorem
Let $k$ be a strictly positive integer.
Let $\lambda$ be a strictly positive real number.
Let $X$ be a continuous random variable with an Erlang distribution with parameters $k$ and $\lambda$.
Then the expectation of $X$ is given by:
- $\expect X = \dfrac k \lambda$
Proof
\(\ds \expect X\) | \(=\) | \(\ds \frac 1 {\lambda^1} \prod_{m \mathop = 0}^0 \paren {k + m}\) | Raw Moment of Erlang Distribution | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac k \lambda\) |
$\blacksquare$