1. Let , , ..., denote the outcomes when rolling n fair dice. Let + ... + equal the sum of these n rolls. Use animation to plot probability histograms for the distribution of . Solution

2. Let , , ..., denote the outcomes when rolling n fair dice. Let + ... + equal the sum of these n rolls. Use animation to plot probability histograms for the distribution of . Superimpose a normal p.d.f. Solution

3. Let , , ..., denote a random sample of size n from the distribution with p.d.f.

f ( x ) = ( x + 1)/6, x = 0, 1, 2. Let + ... + . Use animation to show that the probability histogram of , as n increases, becomes more and more symmetric and can be approximated with a N ( n , n ) p.d.f. Solution