Question: Letbe a Bernoulli random variable that indicates which one of two hypotheses is true, and let. Under the hypothesis, the random variablehas a normal distribution

Letbe a Bernoulli random variable that indicates which one of two hypotheses is true, and let. Under the hypothesis, the random variablehas a normal distribution with mean, and variance. Under the alternative hypothesis,has a normal distribution with meanand variance.

Consider the MAP rule for deciding between the two hypotheses, given that.

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