Question

Consider a murder trial. Two states of nature: θ1=”Guilty”, θ2 =”Innocent”. Two actions for the jury: a1 =”Jail”, a2 =”Free”. The loss function is zero if the jury makes a correct decision. The loss is 5 if the jury let’s a criminal free but it is 10 if an innocent person is sent to jail. Data from DNA is available in the form of a statistical variable X with X|θ1 ∼ N(1, 1/4) and X|θ2 ∼ N(0, 1). Find the Bayes rule under the assumption of equal a priori probabilities. The Bayes rule sends the accused to jail if and only if,

(A) 0 < x < 1

(B) x > 3 4

(C) 1 3 < x < 1

D) 2 3 < x < 2

(E) 1 < x < 2

Answer 1

Solution:

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