Mathematics — Probability · central-limit-theorem-continuous
Problem
How large must n be before Sn=X1+X2+⋯+Xn is approximately normal? This number is often surprisingly small. Let us explore this question with a computer simulation. Choose n numbers from [0,1] with probability density f(x), where n=3,6,12,20, and f(x) is each of the densities in Exercise 7. Compute their sum Sn, repeat this experiment 1000 times, and make up a bar graph of 20 bars of the results. How large must n be before you get a good fit?