Poisson Distribution

The probability mass function of the Poisson distribution is given by:

\[ P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!} \]

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30

Binomial Distribution

The probability mass function of the binomial distribution is given by:

\[ P(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k} \]

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0.5

Geometric Distribution

The probability mass function of the geometric distribution is given by:

\[ P(k; p) = (1-p)^{k-1} p \]

0.5
20

Normal Distribution

The probability density function of the normal distribution is given by:

\[ f(x; \mu, \sigma) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}} \]

0
1

Exponential Distribution

The probability density function of the exponential distribution is given by:

\[ f(x; \lambda) = \lambda e^{-\lambda x} \quad \text{for } x \geq 0 \]

5

Beta Distribution

The probability density function of the beta distribution is given by:

\[ f(x; \alpha, \beta) = \frac{x^{\alpha-1} (1-x)^{\beta-1}}{B(\alpha, \beta)} \quad \text{for } 0 < x < 1 \]

2
5

Gamma Distribution

The probability density function of the gamma distribution is given by:

\[ f(x; \alpha, \beta) = \frac{x^{\alpha-1} e^{-x/\beta}}{\beta^\alpha \Gamma(\alpha)} \quad \text{for } x \geq 0 \]

1
5