Problem 4. A small startup tech company has 4 customer service telephone lines. Let xdenote the number of phone lines in use at any given time. Suppose that the orobabili distribution of x is as follows: 10 noints) 2 a 3 0.31 a.) Determine the value of a if the data above represent a discrete probability distribution. Hint: The probabilities must add-up to 1. b.) Calculate and interpret the expected value of x. Hint: Add-up the xP(x). Column. c.) Calculate the standard deviation of x. Hint: Add-up the x2P(x) Column, then subtract from it the square of the excepted value of x (which you found in b), and then extract the square root from that difference