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.
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?
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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