A Statistics course is comprised of 25 1.5-hour sessions. At the beginning of the semester, the course professor says that as a part of evaluation rubric, he will give some pop quizzes. We use the random variable X to denote the total number of pop quizzes given in this course.
Answer the following questions assuming that the professor gives a quiz on any of the 25 sessions independent of other sessions and that the probability of giving a quiz on any of the 25 days is 0.2:
a. Is X a continuous random variable or a discrete random variable?
b. Fill the blanks with the appropriate values: X ˷ 13 (____, ____)
c. What is the expected number of quizzes during the semester?
d. What is the variance of the number of quizzes during the semester?
e. What is the probability that the professor gives exactly 2 quizzes during the semester?
f. P (3 ≤ X ≤ 5) =?