Let Y = <Y1, Y2, Y3> and let v = <1,2,-3>. Suppose Yi ~ Norm(5,2). What is the distribution of v dot Y?
I know that the dot product of the two vectors is Y1 + 2Y2 - 3Y3. But I don't understand the concept of how to tie the Normal distribution into this result.
Here is a link for getting the sum: Sum of normally distributed random variables - Wikipedia, the free encyclopedia
Getting the difference is very similar (means subtract but the variances still add).