I am new to this site so I'm not quite sure how this whole thing goes. Anyway, I have a question from my homework for statistics class. I'm new to statistics so questions that seem easy to you might be a little bit more difficult for me. I'm having one of those moments where my mind has gone blank. The problem that I'm stuck at is this:
Suppose that $X_1$ and $X_2$ are jointly normally distributed & that $E[X_1] = 1,E[X_2] = 2,var[X_1] = 3,var[X_2] = 4,cov[X_1, X_2] = 1$.
How do you find the distribution of $Y= 1 + 2X_1 + 3X_2$? Thank you ahead of time to those who'll explain this problem to me. I really appreciate your time. Do you treat it kind of like a function and plug in the first values for expected mean. Then do you do the same for variance?