Evidence concerning the guilt or innocence of a defendant in a criminal investigation can be summarized by the value of an exponential random variable X whose mean μ depends on whether the defendant is guilty. If innocent, μ = 1; if guilty, μ = 2. The deciding judge will rule the defendant guilty if X > c for some suitably chosen value of c.
(a) If thejudge wants to be 95 percent certain that an innocent man will not be convicted, what should be the value of c?
(b) Using the value of c found in part (a), what is the probability that a guilty defendant will bc convicted?
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