Sums of Continuous Random Variables

Let [Maple Math] , [Maple Math] , ..., [Maple Math] be a random sample of size n from a continuous distribution with p.d.f. f(x) , where f(x) > 0 for a < x < b and [Maple Math] < a < x < b < [Maple Math] . This section illustrates how MAPLE can be used to find the p.d.f. of the sum of these random variables.

1. [Exercises 5.2.8 and 5.2.9(a) enhanced ] Let f(x) = 1, 0 < x < 1. Show how to find the p.d.f. of [Maple Math] .

2. [Exercise 5.4.9 and Figure 5.2 in Hogg/Tanis] Let f(x) = 1, 0 < x < 1. Find the p.d.f. of [Maple Math] + . . . + [Maple Math] .

3. [Exercise 5.2.8 enhanced ] Let f(x) = [Maple Math] , [Maple Math] < x < 1. Show how to find the p.d.f. of [Maple Math] , [Maple Math] , [Maple Math] . Solution

4. [Exercise 5.4.10 and Figure 5.5 in Hogg/Tanis] Let f(x) = [Maple Math] , [Maple Math] < [Maple Math] < 1. Find the p.d.f. of [Maple Math] + . . . + [Maple Math] . Solution

5. [Exercise 5.2.9] Let f(x) = [Maple Math] , [Maple Math] < x < 1. Show how to find the p.d.f. of [Maple Math] .

6. [Exercise 5.4.11(b) and Figure 5.4 of Hogg/Tanis] Let f(x) = [Maple Math] , [Maple Math] < x < 1. Find the p.d.f. of [Maple Math] + . . . + [Maple Math] .