Combining Random variables

[heburnll]

Ok, this is driving me nuts.

I think I understand # 1, by just plugging in the mean for X and the mean for y into the equation. But # 2 or 3, I don't even know where to start. Can somebody explain what I need to do to solve these?

X~N(4,2) Y~N(3,1)

1. E(2X-3Y+2)=
2. S.D. (2X-3Y+2)=
3. P(2X-3Y+2>1)=

 

[royhaas]

2. Find the variance first, assuming independence.
3. Write the linear combination as one normal, assuming independence.