44. Let X and Y be independent gamma random variables, both with the same scale parameter

b. The value of the other parameter is a1 for X and a2 for Y.

Use moment generating functions to show that X 

Y is also gamma distributed with scale parameter b, X  Y

15 P1X  Y

152 P12 X  Y 12.

and with the other parameter equal to a1  a2. Is X  Y gamma distributed if the scale parameters are different? Explain.