Distribution graph Distribution graph

Description

The experiment consists of selecting a random sample of size $$n$$ from the standard uniform distribution. The first graph shows the probability density function and moments of the sampling distribution in blue. For each run of the experiment, the empirical density function and moments are shown in red. The sample values are shown in the sample table. For a specified $$k$$, the $$k$$th order statistic is displayed on each update in the data table. This order statistic has the beta distribution with parameters $$k$$ and $$n - k + 1$$. The probability density function and moments of $$X_{(k)}$$ are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical probability density function and moments of $$X_{(k)}$$ are shown in red in the distribution graph and are recorded in the distribution table. The parameters $$n$$ and $$k$$ can be varied with the input controls bars.