Answer.

For each lecture the professor chooses between white, yellow, and purple chalk, independently of previous choices. Each day she chooses white chalk with probability 0.5, yellow chalk with probability 0.4, and purple chalk with probability 0.1. a. Suppose we observe this professor for the next 10 days. Define appropriate random variables to count the number of times the professor chooses each color of chalk. Identify by name the marginal distributions, taking care to include any/all relevant parameter(s)! b. Identify the joint distribution of the random variables you defined in part (a) by name (yes, it is a distribution we have encountered before). Be sure to include any/all relevant parameter(s)! c. What is the probability that over the next 10 days she will choose white chalk 5 times, yellow chalk 4 times, and purple chalk 1 time? d. What is the probability that over the next 10 days she will choose white chalk exactly 9 times