Qi Wang, Department of Statistics
Sep 21, 2018
In Eric’s STAT 225 class, 80% of the students passed on Exam 1. If we were to pick a student at random and asked them whether or not they passed, let X be the number of students who passed. What type of random variable is this? How do you know? Additionally, write down the pmf, the expected value, and the variance of X.
Now pick 10 students from Eric’s class, with the same probability of having passed. Let X be the total number of students who passed. What type of random variable is this? What values can X take? Please write down the pmf, the expected value, and the variance of X.
Theorem: Let $X_1, X_2, \cdots, X_n$ be independent Bernoulli random variables, each with the same parameter p. Then the sum $X= X_1 + X_2 + \cdots + X_n$ is a binomial random variable with parameters $n$ and $p$