Probability Distributions

Select Probability Distribution Model

Visualization of Probability Density / Mass Function

Calculation Steps

💡 Mathematical Background of Probability Distributions

Standard Normal Distribution: A bell-shaped continuous probability distribution with mean $\mu = 0$ and standard deviation $\sigma = 1$. The probability density function is given by $f(z) = \frac{1}{\sqrt{2\pi}} e^{-\frac{z^2}{2}}$. Numerical integration is used to calculate the cumulative probability.
Binomial Distribution: A discrete probability distribution representing the number of successes in $n$ independent trials with success probability $p$. The probability mass function is $P(X=k) = {}_n\mathrm{C}_k \, p^k (1-p)^{n-k}$.