(Halloween parade) The city of New York hires you to estimate whether it will rain during the Halloween parade. Checking past data you determine that the chance of rain is 20%. You model this using a random variable \"F with pmf 195(1) = 0-2: 195(0) = 0-8: where '3" = 1 means that it rains and \"F = 0 that it doesn't. Your rst idea is to be lazy and just use the forecast of a certain website. Analyzing data from previous forecasts, you model this with a random variable 11") that satises PM = 1|?\" = 1) = 0.8, Put = 0|? = 0) = 0.75. (a) What is the probability that the website is wrong? Unsatisfied with the accuracy of the website, you look at the data used for the forecast (they are available online). Surprisingly the relative humidity of the air is not used, so you decide to incorporate it in your prediction in the form of a random variable h. 1 (b) Is it more reasonable to assume that fl and 123 are independent, or that they are conditionally independent given 6""? Explain why. You assume that R and 13 are conditionally independent given 6"\". More research establishes that conditioned on F = 1, h is uniformly distributed between 0.5 and 0.7, whereas conditioned on F = 0, it is uniformly distributed between 0.1 and 0.6. (0) Compute the conditional pmf of if given if) and it. Use the distribution to determine whether you would predict rain for any possible value of 11') and h. (d) What is the probability that you make a mistake