(Chad) You nd your coworker Chad really annoying. He often works from home, but when he is in the oice and you walk by his desk he insists on showing you pictures of his pet iguana. You would like to be able to predict when he is in the oice in order to avoid him as much as possible. Another of Chad's annoying habits is to crank up the AC, so you decide to use the temperature in the ofce to predict his presence. After a month you have gathered the following data. Temperature (0 F) No Chad 68 70 68 64 64 (a) You model the temperature using a random variable t. Use a kernel density estimate which is rectangular and has width 2 to estimate the conditional pdf of t given the presence or absence of Chad. Sketch the distribution. (b) We model the presence or not of Chad as a parameter c (c = 1 means he is present, c = 0 that he is absent). If the temperature is 68, does a maximumlikelihood estimate of c predict that Chad is in the oice? (c) Now we take a Bayesian approach and model the presence or absence of Chad using a random variable 5 which is equal to 1 if he is there and 0 if he is not. Estimate the pmf of E from the data. ((1) If the temperature is 64, use the posterior distribution of E to predict whether Chad is in the oice. (e) What problem do we run into if the temperature is 57? Explain how using para metric estimation may alleviate this