use R

Negative Binomial distribution

Suppose a student has 60% chance of scoring a perfect score in an exam with randomly selected questions. The student has to repeatedly take the exam until they achieve three perfect scores.

a) Compute and plot the probability distribution for scoring the three perfect scores (both the PMF and CDF). The student will only go for a maximum of 10 failures before giving up. b) What is the probability that the student will have the three perfect scores with exactly 4 failures?

c) What is the probability that the student will have the three perfect scores with at most 4 failures? d) Simulate the number of failures to get the three perfect scores for 1000 students. Show the barplot of the frequencies of the failures.