b:head_first_statistics:geometric_binomial_and_poisson_distributions
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| b:head_first_statistics:geometric_binomial_and_poisson_distributions [2025/10/13 08:05] – [Geometric Distributions] hkimscil | b:head_first_statistics:geometric_binomial_and_poisson_distributions [2025/10/13 08:59] (current) – [Binomial Distributions] hkimscil | ||
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| Line 739: | Line 739: | ||
| $Var(X) = \displaystyle \frac{q}{p^{2}}$ | $Var(X) = \displaystyle \frac{q}{p^{2}}$ | ||
| + | < | ||
| + | > p <- .4 | ||
| + | > q <- 1-p | ||
| + | > | ||
| + | > p*q^(2-1) | ||
| + | [1] 0.24 | ||
| + | > dgeom(1, p) | ||
| + | [1] 0.24 | ||
| + | > | ||
| + | > 1-q^4 | ||
| + | [1] 0.8704 | ||
| + | > dgeom(0:3, p) | ||
| + | [1] 0.4000 0.2400 0.1440 0.0864 | ||
| + | > sum(dgeom(0: | ||
| + | [1] 0.8704 | ||
| + | > pgeom(3, p) | ||
| + | [1] 0.8704 | ||
| + | > | ||
| + | > q^4 | ||
| + | [1] 0.1296 | ||
| + | > 1-sum(dgeom(0: | ||
| + | [1] 0.1296 | ||
| + | > 1-pgeom(3, p) | ||
| + | [1] 0.1296 | ||
| + | > pgeom(3, p, lower.tail = F) | ||
| + | [1] 0.1296 | ||
| + | > | ||
| + | > 1/p | ||
| + | [1] 2.5 | ||
| + | > | ||
| + | > q/p^2 | ||
| + | [1] 3.75 | ||
| + | > | ||
| + | </ | ||
| Line 789: | Line 822: | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| P(X = r) & = & _{n}C_{r} \cdot p^{r} \cdot q^{n-r} \;\;\; \text{Where, | P(X = r) & = & _{n}C_{r} \cdot p^{r} \cdot q^{n-r} \;\;\; \text{Where, | ||
| - | _{n}C_{r} & = & \frac {n!}{r!(n-r)!} | + | \displaystyle |
| + | \text{c.f., | ||
| + | \displaystyle _{n} P_{r} & = & \displaystyle \dfrac {n!} {(n-r)!} \\ | ||
| \end{eqnarray*} | \end{eqnarray*} | ||
| + | |||
| + | see [[: | ||
| + | |||
| p = 각 시행에서 성공할 확률 | p = 각 시행에서 성공할 확률 | ||
b/head_first_statistics/geometric_binomial_and_poisson_distributions.1760310350.txt.gz · Last modified: by hkimscil