For each of the following random variables, find the interval (r, r+) over which the moment generating function g(r) exists. Determine in each case whether gX(r) exists at the end points r and r+. For...

For each of the following random variables, find the interval (r, r+) over which the moment generating function g(r) exists. Determine in each case whether gX(r) exists at the end points r and r+. For parts a) and b) you should also find and sketch g(r). For part c), g(r) has no closed form.

a) Let , λ,θ be positive numbers and let X have the density