Monte Carlo + CLT

\(\text{Distribution Sampling and CLT Demo}\)

Choose a base distribution, tune its parameters, and vary the sample size \(n\) to see how the standardized average approaches \(N(0,1)\) under the Central Limit Theorem.

Parameters

\(\text{Base Distribution}\)

Select the distribution to sample from.

\(\alpha\)

First parameter.

\(\beta\)

Second parameter.

\(\text{Sample Size } n\)

Each average is computed from 1 i.i.d. draws from the chosen distribution.

Distribution Views

\(\mathrm{Beta}(\alpha,\beta)\)

Histogram of single draws with the theoretical law overlaid.

\(Z_n\)

Histogram of \(Z_n=\dfrac{\bar{X}_n-\mu}{\sigma/\sqrt{n}}\) with the standard normal density.

\(\text{Simulation Size}\)