2. There are 100 animals in a zoo 50 tigers and 50 bears. The weight (in kg) of a tiger follows N (200, 502) and the weight of a bear follows N(300, 502). A Gaussian random variable can be negative and thus the weight can be negative, but let's not worry about it. Let's choose an animal randomly uniformly among the 100. Let Hi = {The chosen animal is a tiger.} and H2 = {The chosen animal is a bear.} be two hypotheses. Let X be the weight of the chosen animal. (a) Plot the posterior distribution pex(12) and Peux (22) as a function of r R. Assume = 1 if H is true and assume = 2 if He is true. (b) Using the MAP rule, decide between Hy and H, given X = I, I ER. At what values of x do you choose Hy and at what values of x do you choose H2? (c) Assume an estimator g(r; 2*) chooses H if x r* given X = I, I E R. Plot the probability of error of the estimator as a function of x*. At what value of r* is the probability of error minimized? How is your answer related to what you observe in (b)? 2. There are 100 animals in a zoo 50 tigers and 50 bears. The weight (in kg) of a tiger follows N (200, 502) and the weight of a bear follows N(300, 502). A Gaussian random variable can be negative and thus the weight can be negative, but let's not worry about it. Let's choose an animal randomly uniformly among the 100. Let Hi = {The chosen animal is a tiger.} and H2 = {The chosen animal is a bear.} be two hypotheses. Let X be the weight of the chosen animal. (a) Plot the posterior distribution pex(12) and Peux (22) as a function of r R. Assume = 1 if H is true and assume = 2 if He is true. (b) Using the MAP rule, decide between Hy and H, given X = I, I ER. At what values of x do you choose Hy and at what values of x do you choose H2? (c) Assume an estimator g(r; 2*) chooses H if x r* given X = I, I E R. Plot the probability of error of the estimator as a function of x*. At what value of r* is the probability of error minimized? How is your answer related to what you observe in (b)