Can anyone explain blue writing? Thank you!! Let Yı and Y2 be independent, Normal random variables,...

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Can anyone explain blue writing? Thank you!!

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Answer 1

Answer #1

Query 1: No Moment generating function is not the only way of getting the density of the linear combination. Jacobian method can also be used for the same.

Query 2:Yes this is a formula and it would be helpful if you could remembe it, But anyway you can readily derieve this if required.

Query 3:

$E(e^{(a_1Y_1)t})\\=E(e^{(a_1t)Y_1}) \\=E(e^{uY_1})\text{ where u=}a_1t \\ = M_{Y_1}(u) \\= M_{Y_1}(a_1t)$

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