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5. (12 points) Consider a sample dataset with the binary response y that takes possible values of 0 and 1 and a single predictor :3. We assume 3 follows a normal distribution with density function mm = k) = 1 exp (o M). 27m where we is the mean of the k-th class, k = 0, 1, or is the variance for both classes. The estimated parameter values for a training data are m = 2, fig = 4, 62 = 3, in = 0.25, fro = 0.75. We now use Linear Discriminant Analysis (LDA) to answer the following question: (a). Predict the posterior probability 15(y = 1|$ = 0). (b). Using your results from (a), make a prediction for the class for x = 0. (Use the default 0.5 as probability threshold for classication) Hint: The formulas for discriminant scores are: 30(93) = a: - '53 7 35 + log(:='rg), 51(56) = :c- 0% 7 2 2&1: + log(fr1). The posterior probability can be written as a 1 emllz . . . 3 as; = llss) = '\"1\\/2_6 \"minted _'3 1'\") fro 1 e'mnlz + 1'71 1 e_%f($_f'1)2 can\") + emf) 2776 2176' Note: the function log() is the natural logarithmic function