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. A graph comparing the standard normal p.d.f. with the p.d.f.s for the t distribution for several values of the degrees of freedom can come alive using animation. Solution

3. A CAS can be used to show that the weighted average of two Cauchy random variables is Cauchy. This in turn can be used to prove that the distribution of X - bar is Cauchy when sampling from a Cauchy distribution. Solution

4. Find the mean and the variance of the beta distribution and animate some beta p.d.f.'s. Solution