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Math Help - normal distribution

  1. #1
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    normal distribution

    need help with this dont know were to start

    question

    suppose X1 and X2 are identically distributed independent standard normal random variables
    <br />
\mu =0, \sigma =1<br />

    write down the joint pdf of (X1, X2). determine the pdf of the linear transformation y1 =2x1-x2, y2=x1-2x2.

    determine the correct range of this random variable.

    any help appreciated
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  2. #2
    MHF Contributor matheagle's Avatar
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    You start with the joint density of X1 and X2.
    Then you solve for X1 and X2 in terms of the Y's.
    You substitute into the first density and you multiply the absolute value of the jacobian.
    This is just like the change to polar in calc3.
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  3. #3
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    thanks

    but how do you solve for x1 and x2.

    abit more help please
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  4. #4
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    mr fantastic's Avatar
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    Quote Originally Posted by kermit View Post
    thanks

    but how do you solve for x1 and x2.

    abit more help please
    y_1 = 2x_1 - x_2 .... (1)

    y_2 = x_1 - 2x_2 .... (2)

    are a pair of linear simultaneous equations and at this level you are well and truly expected to know how to solve such a system. Perhaps use the elimination method ......? Start by multiplying equation (2) by -2 and then adding the two equations together .... ? etc.
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