Suppose the probability mass function for an obsewable variable X is given by: f ( x I A) = (e-AL’)/x!, x = 0, 1,. . . . I . =- 0. Your prior density for i. is given by: g(2} = 2e-2”. You observe X = 3. Test the hypothesis /f(, : i = I , versus the alternative hypothesis H , : i, # 1. Assume that your prior probabilities on the hypotheses are: P{H,} = P{Ho) = 1 /2.