Suppose that X,.. . . ,A’,, are i.i.d. following the law h‘(0,d ).W e assunie that o2 is unknown. Form the sample mean and variance: k =:

I /n X, and 2 = I / n c;(T - 2)’.Y ou observe X = 5, s2 = 37, for n = 50. You adopt the prior distributions: 0 - hr( I , I ) and g( l/02)rx ($)4e-Zui,w ith B and o2 a priori independent. Assume that P(Ho) = 0.75, P { H , ) = 0.25. Test the hypothesis H,, : 0 = 3, versus