1. [Exercise 4.4.1] Let X have a normal distribution with mean m and variance . Find the moment-generating function of X and use it to find the mean and variance of X . Solution

2. [Exercise 4.1.1] Let f ( x ) = , 0 < x < 1. Show that f ( x ) is a p.d.f. and show that m = e - 2 and = 2 e - + 2. Solution

3. [Exercise 2.1.5] Let denote a ball of radius 1 in n -space. Let equal the volume of . Find the values of both empirically and theoretically.

4. [Figure 11.11 (beta p.d.f.'s), Exercise 11.6.14 of Hogg/Tanis] Find the mean and the variance of the beta distribution and animate the beta p.d.f.'s in Figure 11.11. Solution