Question: Prove: If x is a standard normal random variable and if y is a chi- square random variable with k degrees of freedom and IF

Prove: If x is a standard normal random variable and if y is a chi- square random variable with k degrees of freedom and IF x and y are statistically independent, then the random variable t = x /(y/k)1/2 is distributed as a student-t distribution U= 0 k 02 = ,k > 2 T[(k +1/2] (k+1)/2 k - 2 f. (t, k) = +1 a , = \\B, = 0, k> 3 IT NKT(k / 2) k a 4 = B, = 3+0 , k > 4 V-4

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