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Math Help - Dist. of functions of a Random Variable

  1. #1
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    Dist. of functions of a Random Variable

    Hey, all. Having a rough time with a couple of problems, here's one:

    1) If X is chi-squared^2(12); that is, r = 12 sorry dunno the correct notation)

    find constants a and b such that P(a <X<b)=0.90 and p(X<a)=0.05

    ---
    I think I know how to set it up; the probability is given between a & b, so I need to integrate with bounds a & b, and set the integral equal to 0.9; likewise, I can from 0-->a and set it equal to 0.05

    My problem is the integral. Is my pdf correct here:

    f(x)= [x^5e^(-x/2)] / (6)(2^6)

    So I'd be integrating 1/384* integral of x^5e^(-x/2) ??

    How can I do that integral without doing integration by parts 5 times?? Thanks.
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  2. #2
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    Quote Originally Posted by amor_vincit_omnia View Post
    Hey, all. Having a rough time with a couple of problems, here's one:

    1) If X is chi-squared^2(12); that is, r = 12 sorry dunno the correct notation)

    find constants a and b such that P(a <X<b)=0.90 and p(X<a)=0.05

    ---
    I think I know how to set it up; the probability is given between a & b, so I need to integrate with bounds a & b, and set the integral equal to 0.9; likewise, I can from 0-->a and set it equal to 0.05

    My problem is the integral. Is my pdf correct here:

    f(x)= [x^5e^(-x/2)] / (6)(2^6)

    So I'd be integrating 1/384* integral of x^5e^(-x/2) ??

    How can I do that integral without doing integration by parts 5 times?? Thanks.
    Why not use tables of critical values (for 12 degrees of freedom)?

    Pr(X < a) = 0.05 therefore ......

    Pr(X < b) = 0.95 therefore Pr(X > b) = 0.05 therefore .....

    Otherwise you're stuck with the integration ......
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