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 also?