mean_and_variance_of_binomial_distribution
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| mean_and_variance_of_binomial_distribution [2024/10/14 16:47] – [For variance] hkimscil | mean_and_variance_of_binomial_distribution [2024/10/14 17:06] (current) – [For variance] hkimscil | ||
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| Line 94: | Line 94: | ||
| (p+(1-p))^m \\ | (p+(1-p))^m \\ | ||
| \text {and, we also know that it is 1} \\ | \text {and, we also know that it is 1} \\ | ||
| - | (p+(1-p))^m = 1^m | + | (p+(1-p))^m = 1^m \\ |
| & = n(n-1)p^2 (p + (1-p))^m \\ | & = n(n-1)p^2 (p + (1-p))^m \\ | ||
| & = n(n-1)p^2 \\ | & = n(n-1)p^2 \\ | ||
| Line 102: | Line 102: | ||
| E[X(X - 1)] & = n(n-1)p^2 \\ | E[X(X - 1)] & = n(n-1)p^2 \\ | ||
| E[X^2 - X] & = n(n-1)p^2 \\ | E[X^2 - X] & = n(n-1)p^2 \\ | ||
| - | E[X^2]- E[X] & = n(n-1)p^2 \\ | + | E[X^2]- E[X] & = n(n-1)p^2 |
| - | E[X^2]- np & = n(n-1)p^2 \\ | + | E[X^2]- np & = n(n-1)p^2 |
| E[X^2]& = n(n-1)p^2 + np \\ | E[X^2]& = n(n-1)p^2 + np \\ | ||
| \\ | \\ | ||
mean_and_variance_of_binomial_distribution.1728892048.txt.gz · Last modified: 2024/10/14 16:47 by hkimscil