Question

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Stochastic models:

In Fig.B.2 below, suppose C denotes cancerous state and the marginal (prior) probability of occurrence of C is: P(C)-0.01; and, С denotes the non-cancerous state. Further, if the medical treatment is pursued, it is denoted by the state, T; and, when the medical treatment is not administered, it denotes the state, T In relevant medical diagnostic and treatment procedures, there are two possible errors that may occur: Type I and Type II errors and their corresponding conditional probabilities are indicated in the state-diagram/matrix shown below Types of errors denoted by: X States Probability T TError X TypeI Type II of error 0.02 0.05 Specifying the underlving reasons clearly, answer the following: (a) With reference to details in Fig. B.2, define the following probabilities: p(T/C), p(T/C), p(T C) and p(T C) between event sets: C,C and T,T and, explain each of them (b) Determine the following probabilities: p(T) and p(T) using Bayes' rule; and, define/explain these two probabilities. Fig. B.2 Useful hints/formulas 1. The chance of occurrence of an event B, given that A has occurred or the chance of occurrence of event A, given that B has occurred, the joint occurrence can be written in a generalized form. P(AB)-РА)P(BA)-P(B)P(AB) 2. Answer hint: {p(T)-NT/C) (C) +p( T / С)xp(C)-0.0293)

Answer 1

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