The Central Limit Theorem says the sums of independent random variables tend to look normal, no matter what crazy distribution the individual variables have. Let us test this by a computer simulation. Choose independently 25 numbers from the interval [0, 1] with the probability density f(x) given below, and compute their sum S25. Repeat this experiment 1000 times, and make up a bar graph of the results. Now plot on the same graph the density (x) = normal (x, (S25), (S25)). How well does the normal density fit your bar graph in each case?

(a) f(x) = 1.

(b) f(x) = 2x.

(c) f(x) = 3x 2 .

(d) f(x) = 4|x 1/2|.

(e) f(x) = 2 4|x 1/2|.

The Program should be either done in "R" or "Python"