Question

1. In St. Louis, the average amount of rainfall in June is 4.3 inches (meaning the daily mean is 4.3/30 inches). On average, 20 days of June experience no rain at all (meaning the probability of 0 inches of rain on any June day is 20/30). Assume the pdf of inches of rainfall per day is exponential, so that the pdf has the form below. (a) Find a and b (so that E(X)-4.3/30) (b) What is the chance of getting more than 1.5 inches of rain on any day? (c) A tuna can 1.5 inches deep is put outside in an open area in St. Louis and emptied at the same time every day. Let Y be the random variable representing the depth of rainwater in the can just prior to being emptied, for any day in June. (Assume no evaporation. Note: if there is more than 1.5 inches of rainfall, the can overflows and the depth remains at 1.5 inches.) Write the pdf of Y, fy, and then provide rough sketches of both the pdf, fy, and the cdf, Fy

Answer 1