Poisson Distribution PDF Calculator Poisson Distribution PDF Calculator For a Poisson distribution with rate parameter \(\lambda > 0\), the probability mass function is given by: $$ P(X=x)= \frac{\lambda^x\,e^{-\lambda}}{x!},\quad x=0,1,2,\dots $$ * Enter a nonnegative integer \(x\) and a rate \(\lambda\). Step 1: Enter Parameters \(x\) (nonnegative integer): e.g., 3 Rate Parameter, \(\lambda\): e.g., 2 Calculate […]
Read MoreF Distribution Sample Generator F Distribution Sample Generator Generate random samples from an F distribution with degrees of freedom \( d_1 \) and \( d_2 \). The F random variable is generated as: $$ F = \frac{\chi^2_{d_1}/d_1}{\chi^2_{d_2}/d_2}, $$ where \( \chi^2_{d} \) denotes a chi‑square random variable with \( d \) degrees of freedom. * […]
Read MoreF Distribution Mode Calculator F Distribution Mode Calculator For the F distribution with degrees of freedom \( d_1 \) and \( d_2 \), the mode is given by: $$ \text{mode} = \frac{(d_1 – 2)d_2}{d_1(d_2 + 2)} \quad \text{for } d_1 > 2. $$ * Enter the degrees of freedom (\( d_1 > 0 \) and […]
Read MoreF Distribution Mean Calculator F Distribution Mean Calculator For the F distribution with degrees of freedom \( d_1 \) and \( d_2 \), the mean is given by: $$ \mu = \frac{d_2}{d_2 – 2} \quad \text{for } d_2 > 2. $$ * Enter the degrees of freedom (\( d_1 > 0 \) and \( d_2 […]
Read MoreF Distribution Inverse CDF Calculator F Distribution Inverse CDF Calculator For the F distribution with degrees of freedom \( d_1 \) and \( d_2 \), the cumulative distribution function is given by: $$ F(x; d_1, d_2) = I\left(\frac{d_1 x}{d_1 x + d_2}; \frac{d_1}{2}, \frac{d_2}{2}\right), \quad x \ge 0. $$ The inverse CDF finds the value […]
Read MoreF Distribution CDF Calculator F Distribution CDF Calculator For the F distribution with degrees of freedom \( d_1 \) and \( d_2 \), the cumulative distribution function is given by: $$ F(x; d_1, d_2) = I\left(\frac{d_1 x}{d_1 x + d_2}; \frac{d_1}{2}, \frac{d_2}{2}\right), \quad x \ge 0. $$ * Enter the F-value (\( x \ge 0 […]
Read MoreF Distribution PDF Calculator For the F distribution with degrees of freedom \( d_1 \) and \( d_2 \), the probability density function is given by: $$ f(x; d_1, d_2) = \frac{1}{B\left(\frac{d_1}{2},\frac{d_2}{2}\right)} \left(\frac{d_1}{d_2}\right)^{\frac{d_1}{2}} x^{\frac{d_1}{2}-1} \left(1 + \frac{d_1}{d_2}x\right)^{-\frac{d_1+d_2}{2}}. $$ * Enter the F-value (\( x \)) and the degrees of freedom (\( d_1 > 0 \) […]
Read MoreUniform Distribution Variance Calculator Uniform Distribution Variance Calculator For a uniform distribution over the interval \([a,b]\), the variance is given by: $$ \sigma^2 = \frac{(b-a)^2}{12}. $$ * Enter the minimum value \(a\) and the maximum value \(b\) (with \(a < b\)). Step 1: Enter Parameters Minimum, \(a\): e.g., 0 Maximum, \(b\): e.g., 10 (must be […]
Read MoreUniform Distribution Sample Generator Uniform Distribution Sample Generator Generate random samples from a Uniform distribution defined over the interval \([a, b]\). Each sample is computed using: $$ x = a + (b-a) \, U, $$ where \(U\) is uniformly distributed over \([0,1]\). * Enter the minimum value \(a\), maximum value \(b\) (with \(a < b\)), […]
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