Standard normal, Chi-square and Student's t distribution relationship

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Z has a standard normal distribution and U has a Chi-square distribution with k degrees of freedom. If Z and U are independent, then the transformation X = k U Z and Y = U shows that X has a Student's t distribution with k degrees of freedom.

(CLO4) Q2. If Z has a standard normal distribution and U has a Chi-square distribution with k
degrees of freedom, and if Z and U are independent, then show that k U Z has a Student's t
distribution with k degrees of freedom. Proof: H.W (Hint: use the transformation technique (Let
X = k U Z and Y = U ) ) (1 mark)

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