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Math Help - a little linear algebra with a normal distribution

  1. #1
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    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.
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    Quote Originally Posted by ecc5 View Post
    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?
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  3. #3
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    Umm no I'm not completely sure. It's been a while.
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    Quote Originally Posted by ecc5 View Post
    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).
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  5. #5
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    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?
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    Quote Originally Posted by ecc5 View Post
    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.
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