2. Let X be a random variable with distribution Po(X < x) = 1 – e-(2/0)2 for x > 0, е where 0 > 0. (a) Consider testing

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2. Let X be a random variable with distribution Po(X < x) = 1 – e-(2/0)2 for x > 0, е where 0 > 0. (a) Consider testing Ho : 0 = 0, versus Hj :0 > 0, for some positive constant oo. We reject Ho if X > k. What choice of k would result in a size a test? (b) Consider the class of tests given in (a). Suppose that = 2 and the observed value of X is 0.971. What is the observed p-value? (c) Construct an 80% confidence interval for 0 that takes the form of (0.2X/c, X/c) for some positive constant c. What value can c take? You can use the fact that (0.8043)(1- 0.804324) = 0.8. =