# Thread: a little linear algebra with a normal distribution

1. ## a little linear algebra with a normal distribution

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.

2. Originally Posted by ecc5
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.
Get the distribution of the random variable $\displaystyle X = Y_1 + 2Y_2 - 3Y_3$. I assume you know how to do this?

3. Umm no I'm not completely sure. It's been a while.

4. Originally Posted by ecc5
Umm no I'm not completely sure. It's been a while.
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).

5. Oh yeah!!! This is coming back to me.

So here's what I got: Norm(0,sqrt(56)).

I got the standard deviation by doing: sqrt(4+4*4+9*4).

Does that look/sound right?

6. Originally Posted by ecc5
Oh yeah!!! This is coming back to me.

So here's what I got: Norm(0,sqrt(56)).

I got the standard deviation by doing: sqrt(4+4*4+9*4).

Does that look/sound right?
No. Wrong variance.