PROBLEM 1 Consider two independent positive random variables X and Y, where their first and second moments are respectively given by E[X] = 2 E[X²] = 5 and JE[Y] = 3 | E[Y²] = 11 Find (a) E[2X + 3Y]; (b) Var (2X-3Y).

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PROBLEM 1
Consider two independent positive random variables X and Y, where their
first and second moments are respectively given by
E[X] = 2
E[X²] = 5
and
JE[Y] = 3
| E[Y²] = 11
Find
(a) E[2X +3Y];
(b) Var(2X - 3Y).
Transcribed Image Text:PROBLEM 1 Consider two independent positive random variables X and Y, where their first and second moments are respectively given by E[X] = 2 E[X²] = 5 and JE[Y] = 3 | E[Y²] = 11 Find (a) E[2X +3Y]; (b) Var(2X - 3Y).
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