13. Suppose X has the following probability distribution. i. Verify that this is a valid probability distribution. ii. Find the mean of X. iii. Find the variance of X. iv. Based on your answer from part [ii], what is the mean of 7X + 6 v. Suppose another random variable Y has a mean of -2. What is the mean of 2X + Y? 14. Data on 1,000 executives at a marketing firm were collected and are summarized below. There are 3 levels of salary at this company. 30,000 60,000 .4-5 .40 i. What is the mean salary at this company? ii. If everyone is given a 15,000 dollar raise, what is the new expected salary? iii. If everyone takes a pay cut of 5,000 dollars, what is the new expected salary? iv. What is the probability that a worker here makes 90,000 dollars? v. What is the probability that a worker here makes more than 90,000 dollars? What is the probability that a worker here makes less than 90,000 dollars