Description

The experiment consists of selecting a random sample \(\bs{X} = \left(X_1, X_2, \ldots, X_n\right)\) of size \(n\) from a specified distribution. The following sampling distributions can be selected with the list box:

• The standard uniform distribution, that is, the uniform distribution on the interval \([0, 1]\)
• The standard exponential distribution, that is, the exponential distribution with parameter 1

Random vector \(\bs{Y} = \left(X_{(1)}, X_{(2)}, \ldots, X_{(n)}\right) \) denotes the sequence of order statistics. The first graph shows the probability density function of the sampling distribution while the second graph shows the probability density function of the \(k\)th order statistic \(X_{(k)}\) for a specified \(k\). The parameters \(n\) and \(k\) can be varied with the input controls.