Part4) Poisson distribution (20 points) Suppose that, on an average, students email 10 questions per day to the professor. a) What is the probability that the professor will have to answer exactly 8 questions per day? b) What is the probability that the professor will have to answer at most 8 questions per day? c) What is the probability that the professor will have to answer between 6 and 12 questions (inclusive)? d) Calculate and plot the PMF for the first 20 questions. e) Suppose the course runs for 50 days. Simulate the number of questions the professor gets per day over the course run. Show a barplot of the frequencies of the number of questions. Show a boxplot of the number of questions. What do you infer from the plots