2.12 Suppose that the random variable X N(0, 1), and that ( 1 2 , 2 ), where is a

2.12 Suppose that the random variable X ∼ N(0, θ−1), and that θ ∼ Γ( 1 2 , 2

γ ), where γ is a positive integer. Show that the marginal distribution of X is the t-distribution, tγ.