Discrete Distributions 1. A pair of fair dice is rolled, and the sum of their faces is recorded. The probabilities of each sum are recorded in the table below. Answer the questions that follow. If you...

Extracted text: Discrete Distributions 1. A pair of fair dice is rolled, and the sum of their faces is recorded. The probabilities of each sum are recorded in the table below. Answer the questions that follow. If you do it by hand, show all your work here. If you use Excel, make sure you include a screenshot of your work here. 7 10 11 | 12 2 3 4 5 6 8 9 P(X=x) 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36 a. What is the probability that the sum of the faces shown is greater than 9? b. Which sum is most likely? Which sum is least likely? c. Calculate the expected value (mean) of X. d. Calculate the standard deviation of X.