Statistics Problem

Hello, I am trying to solve the problem below but am not sure how to go about it. Does anyone have any ideas or advice on how to solve this problem?

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

-------------- ~ t(C6)

Thank you!


TS Contributor
Since this question is relating ratio of normals and t-distribution, the only thing come up in my mind is Cauchy distribution.


Ambassador to the humans
Do you know how one can express a T distribution as a ratio of a random variable with a normal distribution and a random variable with a chi-square distribution?