Question: 4.2 In (4.8) (i) Derive the joint probability density function of (Y,Z). (ii) Consider the transformation (Y,Z) (T,Z) and derive the joint probability density

4.2 In (4.8) (i) Derive the joint probability density function of (Y,Z). (ii) Consider the transformation (Y,Z) → (T,Z) and derive the joint probability density function of (T,Z) (using the change of variable formula (Theorem A.6)). (iii) Show that the probability density function of T (the probability density function of t(n)-distribution) is given by

f(t) = (n+1) n () + n -

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