For This Question You May Assume That Linear Combinations of Normal

Essay

For this question you may assume that linear combinations of normal variates are
themselves normally distributed.Let a, b, and c be non-zero constants.
(a) $$X \text { and } Y \text { are independently distributed as } N \left( a , \sigma ^ { 2 } \right) \text {. What is the distribution of } ( b X + c Y ) \text { ? }$$