Check the validity of the central-limit theorem by repeatedly generating n independent uniformly distributed random variables in the interval (-0:5, 0:5), forming the sum given by (5.187), and plotting the histogram. Do this for N = 5, 10, and 20. Can you say anything qualitatively and quantitatively about the approach of the sums to Gaussian random numbers? Repeat for exponentially distributed component random variables (do Computer Exercise 5.1 first). Can you think of a drawback to the approach of summing uniformly distributed random variables to generating Gaussian random variables? (Hint: Consider the probability of the sum of uniform random variables being greater than -0:5N or less than -0:5N. What are the same probabilities for a Gaussian random variable?)
In this exercise we examine a useful technique for generating a set of samples having a given pdf.
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