(2) Solve the following problems related to the expectation of known distributions. (a) [lpt] A student takes the test consists of 100 questions. Each question is a multiple choices with ve options. Only one of the options are the correct answer. Obviously, the answers of the questions are not related to each other. What is the expectation of the questions student gets right in the test? (b) [2pts] A student is waiting for the bus on the bus stop on the morning. If the bus is not cancelled, it comes every 12 minutes. However, each bus can be cancelled with the probability of 20%. rI'he cancellation of the buses are independent. What is the expectation of the waiting time for the students to take the bus? (Obviously, the student takes the rst bus arrives.) (c) [2pts] A store sells two products A and B. The number of A sold in an hour is denoted by X A, where XA has the Poisson()\\A) distribution. Similarly, let XB denote the number of B sold in an hour, where X B has the Poisson()\\3) distribution. The store is open for 10 hours, from 10 am to 6 pm. Each day, the expected value of the total number of items sold is 60 and the expected value of the difference in the number of A sold and the number of B sold (XA X B) is 20. Find the expected values of X A and X B