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Thread: help with t distribution and chi square distribution

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    help with t distribution and chi square distribution




    Let X~N(3,5) and Y~N(-7,2) be independent. Find values of C1,C2,C3,C4,C5,C6 such that

    C1(X+C2)^C3
    -------------- ~ t(C6)
    (Y+C4)^C5

    My attempt

    so the t distribution can become X/sqrt(Y/C6)
    so Y is a chi squared distribution with C6 degrees of freedom

    so if I do
    C2=0
    C3=1
    C1=sqrt(4*C6)
    C4=7
    C5=0.5

    i get

    sqrt(4*C6)(X+0)^1
    -------------- ~ t(C6)
    (Y+7)^0.5

    X
    -------------- ~ t(C6)
    1/[sqrt(4*C6)] * sqrt(Y+7)

    X
    -------------- ~ t(C6)
    sqrt([Y+7]/[4C6])

    here since Y~N(-7,2), and in the equation the mean is being subtracted and then its being divided by its sd, it gets normalized

    X
    ----------- ~ t(C6)
    sqrt(Y/C6)

    X
    ----------- = X/sqrt(Y/C6)
    sqrt(Y/C6)


    Is this right?
    Does X have to be standardized?

  2. #2
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    Re: help with t distribution and chi square distribution


    omega, as the t-distribution on the RHS is not fully specified, I think this is open end question and have more than one set of answers.

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