# 2/22/2023

## Poisson Distribution

• Briefly discuss the general form of the probability distribution
• We are looking at a random variable that records the number of events for a large population where the events occur independently of one another. For example, arrivals at an airport, accidents at an intersection, calls to a customer service line, etc.
• Mean and Variance are both equal to lamda
• Use dpois(), ppois(), and qpois() in R

## Class Exercises

4.31, 4.33, 4.37 (find the exact and approximate probability), 4.39, 4.43, and 4.45

A selective college would like to have an entering class of 1200 students. Since not all students who are offered admission accept, the college admits more than 1200 students. Past experience indicates that about 70% of the students admitted will accept the offer of admission. The college decides to admit 1500 students. Assume that students make their decisions independently. Let X denote the number of students who accepted the offer. What is the distribution of X? Find the mean and standard deviation of X. Find the probability that at least 1000 students accept. What is the probability that the college gets more students than they want?