1. [Exercises 10.1.1 and 10.1.2] Define the p.d.f. for the r th order statistic in a random sample of size n for a given distribution function. Then use animation to graph the p.d.f.'s of the order statistics, , , ..., from the U (0, 10) distribution. Solution

2. [Exercise 10.1.5] Define the p.d.f. for the r th order statistics in a random sample is size n for a given distribution function. Then use animation to graph the p.d.f.'s of , ..., when sampling from the exponential distribution with mean . Also find the respective means of the order statistics as well as the respective values of E [ F ( )].

3. [Questions and Comments 10.1.4] There are times when we may be interested in simulating observations of only the first m order statistics out of a random sample of size n . This is illustrated using the U (0, 10) distribution. Solution

4. [Exercise 10.1.7 and Questions and Comments 10.1.4] Suppose we want to make some inference about the mean, , for the exponential distribution using only the first m out of n order statistics. It is useful to know that has a chi-square distribution with 2* m degrees of freedom. This is illustrated empirically. Solution

5. [Questions and Comments 10.1.5] There are times when we may be interested in simulating observations of only the last m order statistics for a random sample of size n . This is illustrated for the U (0, 10) distribution with n = 9 and m = 4.