Part3) Hypergeometric distribution (20 points) Suppose that your professor created a pool of 60 multiple choice questions and 40 programming questions for the final exam. For each student, a random set of 20 distinct questions from the pool will be presented during the exam. The student has the opinion that the multiple-choice questions are easy to handle than the programming questions. a) Compute and plot the probability distribution for the number of multiple choice questions out of the 20 questions that the student will be given? b) What is the probability that the student will have exactly 10 multiple choice questions out of the 20 questions in the exam? c) What is the probability that the student will have at least 10 multiple choice questions out of the 20 questions in the exam? d) Simulate the number of multiple choice questions for 1000 students. Show the barplot of the frequencies of the multiple-choice questions. 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