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--- mean_and_variance_of_poisson_distribution [2020/11/21 02:15] – [Variance] hkimscil
+++ mean_and_variance_of_poisson_distribution [2020/11/21 02:22] (current) – hkimscil
@@ Line 1: / Line 1: @@
+====== Mean and Variance of Poisson Distribution ======
 ====== Mean ======
 Mean Poisson distribution = $\lambda$
@@ Line 81: / Line 82: @@
 \end{eqnarray*}
+따라서
+\begin{eqnarray*}
+E[X(X-1)] & = & E[X^2-X] = E(X^2) - E(X) \\
+& = & \lambda^2  \\
+E(X^2) & = & \lambda^2 + \lambda \\
+\end{eqnarray*}
+다시 원래대로 돌아가서
+\begin{eqnarray*}
+Var(X) & = & E \left[(X-\mu)^2 \right]  \\
+& = & E(X^2) - \left[E(X) \right]^2 \\
+& = & \lambda^2 + \lambda - \lambda^2 \\
+& = & \lambda
+\end{eqnarray*}