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SOLVED: Bayesian InferenceAssume we use a medical device to detect a type of rare cancer. Denote by X ∈ 0,1 if the cancer actually exists in a patient and Y ∈ 0,1 the output of the medical device. Denote by α the false negative and β the false positive of the device; that is,α = P(Y = 0 | X = 1)β = P(Y = 1 | X = 0)where P denotes probability. In addition, denote by π the probability that this cancer happens in the population; this defines a prior distribution of X, that is, π = P(X = 1

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