# a little linear algebra with a normal distribution

• March 9th 2011, 03:52 PM
ecc5
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.
• March 9th 2011, 04:42 PM
mr fantastic
Quote:

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 $X = Y_1 + 2Y_2 - 3Y_3$. I assume you know how to do this?
• March 9th 2011, 06:44 PM
ecc5
Umm no I'm not completely sure. It's been a while.
• March 9th 2011, 07:49 PM
mr fantastic
Quote:

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).
• March 9th 2011, 08:28 PM
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?
• March 10th 2011, 12:29 AM
mr fantastic
Quote:

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.