1. Without the knowledge of independence, we cant solve this problem. So assuming $\displaystyle {X_i}$ are all independent.

$\displaystyle Y = \sum_{i=0}^{i=n} a_i X_{i} \implies \mathbb{E}(Y) = \sum_{i=0}^{i=n} a_i \mathbb{E}(X_{i})$and $\displaystyle \text{Var}(Y) = \sum_{i=0}^{i=n} a_i ^2 \text{Var}(X_{i})$

2. Without independence we could still solve it if we knew that $\displaystyle ({X_1},...,{X_n})$ was a Gaussian vector (which is not implied by the $\displaystyle {X_i}$ being all Gaussians). In that case, the mean of $\displaystyle Y$ would be the same, but its variance would be different (you should take covariances into account).

3. Originally Posted by EconMax Without independence we could still solve it if we knew that $\displaystyle ({X_1},...,{X_n})$ was a Gaussian vector (which is not implied by the $\displaystyle {X_i}$ being all Gaussians). In that case, the mean of $\displaystyle Y$ would be the same, but its variance would be different (you should take covariances into account).
I am really confused, can u please explain what u mean. 4. Originally Posted by nerdo I am really confused, can u please explain what u mean. Post #2 has what you need.

5. Originally Posted by mr fantastic Post #2 has what you need.

I have tried to do this question, and i just don't know were to start, could some1 please just help me I would really appriate it.

6. Originally Posted by nerdo I have tried to do this question, and i just don't know were to start, could some1 please just help me I would really appriate it.
Have you tried to do what post #2 says? What have you done so far, where are you stuck?

7. Originally Posted by mr fantastic Have you tried to do what post #2 says? What have you done so far, where are you stuck?

I don't understand what is meant by "Gaussian vector", i tried to reasearch but still do not understand, and i don't know how to appoarch the question.

8. Originally Posted by nerdo I don't understand what is meant by "Gaussian vector", i tried to reasearch but still do not understand, and i don't know how to appoarch the question.
I said read post #2. Not #3.

9. Originally Posted by mr fantastic I said read post #2. Not #3.
Oh sorry about that, my bad, .

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