Write a program in \(\mathrm{R}\) that simulates \(b\) samples of size \(n\) from a distribution that has distribution function

\[F(x)= \begin{cases}0 & x

For each sample, compute the sample quantile \(\hat{\xi}_{1 / 4}\). When the \(b\) samples have been simulated, a histogram of the \(b\) sample values of \(\hat{\xi}_{1 / 4}\) should be produced. Run this simulation for \(n=5,10,25,50\), and 100 with \(b=10,000\) and discuss the resulting histograms in terms of the theoretical result of Example 4.42.

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Example 4.42. Suppose that {X} is a sequence of independent random variables that have a common distribution F given by F(x)= 12121 x < 0, 0x < (3x-1) < < 1, x 1.