1. [Exercise 5.2.2] 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 . Solution

2. [Exercise 5.5.11] Let , , ..., denote the outcomes when rolling n fair m -sided dice. Let + ... + equal the sum of these n rolls. Use animation to plot probability histograms for the distribution of . Superimpose an approximating normal p.d.f. Solution

3. [Exercise 5.2.4 and Exercise 5.2.17 of Hogg/Tanis] The power of the probability-generating function (factorial moment-generating function) for determining a p.d.f. can be illustrated with a very simple problem. Let X equal the number of times that an n -sided die must be rolled to observe each face at least once. The probability-generating function of X , as a function of t , is . A CAS can expand h = h ( t ) and list the respective probabilities,

P ( ), the coefficients of i n the expansion.