In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

Shiny dashboard "Statistical foundations of machine learning"

Law of large numbers

Convergence of frequency

The upper figure illustrates the convergence of the frequency (\hat{p}) to the probability $p$.

If the frequency $\hat{p}$ is not near 1 or 0 and then sample size $N$ is sufficiently large then the $1-\alpha$ confidence interval is

$$\hat{p} \pm z_{1-\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{N}} $$ Green horizonal lines show the confidence interval for $\alpha=0.01$.

Convergence of the difference between number of heads and tails

The lower figure shows that for $p=0.5$ the number of heads does not converge to the number of tails, or equivalently that the difference between those two numbers does not converge to zero.

gbonte/gbcode documentation built on Feb. 27, 2024, 7:38 a.m.