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b:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/19 17:41] – [Geometric Binomial and Poisson Distributions] hkimscilb:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/19 19:00] (current) – [Geometric Binomial and Poisson Distributions] hkimscil
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 정리  정리 
 \begin{align*} \begin{align*}
-\text{Geometric Distribution:  } \;\;\; \text{X} & \thicksim \text{Geo(p)\\+\text{Geometric Distribution:  } \;\;\; \text{X} & \thicksim Geo(p) \\
 p(X = k) & = q^{k-1} \cdot p \\ p(X = k) & = q^{k-1} \cdot p \\
 E\left[ X \right] & = \frac{1}{p} \\ E\left[ X \right] & = \frac{1}{p} \\
 V\left[ X \right] & = \frac{q}{p^2} \\ 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*} \end{align*}
- 
-\begin{align*} 
-\text{Binomial Distribution:  } \;\;\; \text{X} & \thicksim \text{B(p)} \\ 
-p(X = k) & = \binom{n}{k} \cdot p^{k} \cdot q^{n-k} \\ 
-E\left[ X \right] & = \frac{1}{p} \\ 
-V\left[ X \right] & = \frac{q}{p^2} \\ 
-\end{align*} 
- 
  
 ===== Geometric Distributions ===== ===== Geometric Distributions =====
b/head_first_statistics/geometric_binomial_and_poisson_distributions.1697704881.txt.gz · Last modified: 2023/10/19 17:41 by hkimscil

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