b:head_first_statistics:geometric_binomial_and_poisson_distributions
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b:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/19 17:41] – [Geometric Binomial and Poisson Distributions] hkimscil | b:head_first_statistics:geometric_binomial_and_poisson_distributions [2023/10/19 18:55] – [Geometric Binomial and Poisson Distributions] hkimscil | ||
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\begin{align*} | \begin{align*} | ||
- | \text{Geometric Distribution: | + | \text{Geometric Distribution: |
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: | ||
+ | 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: | ||
+ | P(X=r) & = e^{- \lambda} \dfrac{\lambda^{r}} {r!} \\ | ||
+ | E\left[ X \right] & = \lambda \\ | ||
+ | V\left[ X \right] & = \lambda \\ | ||
\end{align*} | \end{align*} | ||
- | |||
- | \begin{align*} | ||
- | \text{Binomial Distribution: | ||
- | 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.txt · Last modified: 2023/10/19 19:00 by hkimscil