Problem 1: For a one dimensional 2-class problem with 2 actions a1, a2, (a1: choose @1; a2 choose 02). We assume P@1) = 3/5, P(62) = 2/5, conditional densities px|w1) ~ N(0, 1) and p(x|) ~ N(2,4), where N(u, o) is Normal distribution, u is mean and o- is variance. 1. Sketch the likelihood function for each class (ref. Figure 2.1). Calculate the likelihood value for each class if x=5. 2. Sketch the evidence distribution. Calculate the evidence value if x=5. 3. Sketch the posterior probability function for each class (ref. Figure 2.2). Calculate the posterior probability value for each class if x=5. 4. Sketch the likelihood ratio function (ref. Figure 2.3). Calculate the likelihood ratio value if x=5. 5. Calculate the likelihood ratio threshold for zero-one loss function, i.e. maximum posterior classification 6. Calculate the likelihood ratio threshold for the following risk matrix | a 0 4 0 7. Following 1.6, sketch the Bayes risk (conditional risk R(qilx) associated with the action a; according to observation x) as a function of x. Calculate the Bayes risk value if x=5. a22 Problem 1: For a one dimensional 2-class problem with 2 actions a1, a2, (a1: choose @1; a2 choose 02). We assume P@1) = 3/5, P(62) = 2/5, conditional densities px|w1) ~ N(0, 1) and p(x|) ~ N(2,4), where N(u, o) is Normal distribution, u is mean and o- is variance. 1. Sketch the likelihood function for each class (ref. Figure 2.1). Calculate the likelihood value for each class if x=5. 2. Sketch the evidence distribution. Calculate the evidence value if x=5. 3. Sketch the posterior probability function for each class (ref. Figure 2.2). Calculate the posterior probability value for each class if x=5. 4. Sketch the likelihood ratio function (ref. Figure 2.3). Calculate the likelihood ratio value if x=5. 5. Calculate the likelihood ratio threshold for zero-one loss function, i.e. maximum posterior classification 6. Calculate the likelihood ratio threshold for the following risk matrix | a 0 4 0 7. Following 1.6, sketch the Bayes risk (conditional risk R(qilx) associated with the action a; according to observation x) as a function of x. Calculate the Bayes risk value if x=5. a22