13.4 Exercise 8

Use the moment generating function for the symmetric triangular distribution on $\left(- c , c\right)$ as derived
in the section "Three Basic Transforms".

1. Obtain an expression for the symmetric triangular distribution on $\left(a , b\right)$ for any $a < b$.
2. Use the result of part (a) to show that the sum of two independent random variables uniform on $\left(a , b\right)$ has symmetric triangular distribution on $\left(2 a , 2 b\right)$.