topic: mathematical expectation

B. Determine the Expected value of the following situation below. 1. A car insurance company provides insurance that pays P 500,000 to its members for cases for theft or total damage to the car. The probability of paying out the total amount of coverage is 0.06% and the insurance coverage costs the car owner P 24,000. If X is a random variable that represents the company's proceeds from each sold insurance policy, a. Find the expected value of x; b. Based on your answer in (a), I you were a car owner, would you buy an insurance policy from this company? Why or why not? 2. At a car wash, an attendant is paid according to the number of cars that are serviced during his shift. If X is the amount of income the attendant receives over a two hour period, compute the employees expected earnings for two hours. The probability distribution of X is shown below. 3. A medical representative for a pharmaceutical company has two appointments for that day. Based on previous experiences, he believes that he has a 60% chance of closing the deal with his rst appointment and earns P 5,000 in commission. On his second appointment. he believes that he only has 45% chance of closing the deal but he can earn a commission of P 8,000. Assume that the decisions on the two appointments are independent. a. If X is the random variable representing his earnings from the two appointments, construct the probability mass function of X. b. Compute the medical representative's expected income from the two appointments