The command x = runif(1e6)

generates one million random numbers between 0 and 1. Investigate the shape of the histogram of simple transformations of x, using common functions such as log(x), x 2

,

√

x. For example, you can generate a histogram of log(x) using the command hist(log(x), prob=T)

Try to find functions that give different histogram shapes, e.g., curved up, curved down, heaped, or U-shaped. Can you figure out what it is about the functions that generates the shapes you see?