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) $$X \text { and } Y \text { are independently distributed as } N \left( a , \sigma ^ { 2 } \right) \text {. What is the distribution of } ( b X + c Y ) \text { ? }$$

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The Answer of 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) $$X \text { and } Y \text { are independently distributed as } N \left( a , \sigma ^ { 2 } \right) \text {. What is the distribution of } ( b X + c Y ) \text { ? }$$

For This Question You May Assume That Linear Combinations of Normal