i 3 points find the joint distribution of y x xn and y2x xn you can ei

Question

(i) (3 points) Find the joint distribution of Y₁ = X₁ Xn and Y2X₂-Xn. You can either give the probability density function or identify itas a commonly known family of distributions.
(iii) (0.5 point) Consider the case of n = 3. Find whether T3 has a chi-square distribution subject to a multiplicative constant (that is, distributed as bW where b is a constant and W has a chi-square distribution). Justify your answer.