mean_and_variance_of_geometric_distribution
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| mean_and_variance_of_geometric_distribution [2024/10/09 08:18] – [Variance] hkimscil | mean_and_variance_of_geometric_distribution [2025/10/01 13:17] (current) – [Mean] hkimscil | ||
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| ====== Mean and Variance of Geometric Distribution ====== | ====== Mean and Variance of Geometric Distribution ====== | ||
| + | 기하분포의 평균, 그리고 분산 | ||
| ====== Mean ====== | ====== Mean ====== | ||
| 기대값 E(X)는 아래처럼 배웠고. | 기대값 E(X)는 아래처럼 배웠고. | ||
| + | |||
| \begin{align} | \begin{align} | ||
| E(X) & = \sum_{k=1}^{\infty} k \cdot P(X=k) \nonumber \\ | E(X) & = \sum_{k=1}^{\infty} k \cdot P(X=k) \nonumber \\ | ||
| \end{align} | \end{align} | ||
| + | |||
| $P(X=k) $가 geometric distiribution에서는 $q^{(k-1)} \cdot p $ 이므로 $E(X)$는 아래와 같다. | $P(X=k) $가 geometric distiribution에서는 $q^{(k-1)} \cdot p $ 이므로 $E(X)$는 아래와 같다. | ||
| Line 34: | Line 37: | ||
| (1-(1-p))E(X) & = p \frac {1 - (1-p)^k} {1-(1-p)}, \;\;\; \text{because | (1-(1-p))E(X) & = p \frac {1 - (1-p)^k} {1-(1-p)}, \;\;\; \text{because | ||
| & = p \frac {1}{1-(1-p)} \\ | & = p \frac {1}{1-(1-p)} \\ | ||
| + | & = 1 \\ | ||
| p \cdot E(X) & = 1 \\ | p \cdot E(X) & = 1 \\ | ||
| \therefore \quad E(X) & = \frac {1}{p} \\ | \therefore \quad E(X) & = \frac {1}{p} \\ | ||
mean_and_variance_of_geometric_distribution.1728429492.txt.gz · Last modified: by hkimscil