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--- b:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/18 14:37] – [From a scratch (Proof of Binomial Expected Value)] hkimscil
+++ b:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/19 19:00] (current) – [Geometric Binomial and Poisson Distributions] hkimscil
@@ Line 1: / Line 1: @@
 ====== Geometric Binomial and Poisson Distributions ======
+정리
+\begin{align*}
+\text{Geometric Distribution:  } \;\;\; \text{X} & \thicksim Geo(p) \\
+p(X = k) & = q^{k-1} \cdot p \\
+E\left[ X \right] & = \frac{1}{p} \\
+V\left[ X \right] & = \frac{q}{p^2} \\
+\\
+\text{Binomial Distribution:  } \;\;\; \text{X} & \thicksim B(n, p) \\
+p(X = r) & = \binom{n}{r} \cdot p^{r} \cdot q^{n-r} \\
+E\left[ X \right] & = {n}{p} \\
+V\left[ X \right] & = {n}{p}{q} \\
+\\
+\text{Poisson Distribution:  } \;\;\; \text{X} & \thicksim P( \lambda ) \\
+P(X=r) & = e^{- \lambda} \cdot \dfrac{\lambda^{r}} {r!} \\
+E\left[ X \right] & = \lambda \\
+V\left[ X \right] & = \lambda \\
+\end{align*}
 ===== Geometric Distributions =====
@@ Line 924: / Line 942: @@
 ==== From a scratch (Proof of Binomial Expected Value) ====
-[[:Mean and Variance of Binomial Distribution|Mathematical proof of Binomial Distribution Expected value and Variance]]
+[[:Mean and Variance of Binomial Distribution|이항분포에서의 기댓값과 분산에 대한 수학적 증명]], Mathematical proof of Binomial Distribution Expected value and Variance
 ====== Poisson Distribution ======
 $$X \sim Po(\lambda)$$