Extracted text: Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die. a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x. b. Calculate the variance of x. c. Calculate the standard deviation of x. a. List the possible outcomes for the variable x. Choose the correct answer below. O A. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 O B. 1, 2, 3, 4, 5, 6 O C. 3, 4, 5, 6, 7, 8, 9, 10, 11 O D. 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Determine the probability for each outcome. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or fractions.) O A. P(1)= P(2) =, P(3) =, P(4)=, P(5) =, P(6) = P(7) =, P(8) = P(9) =, P(10)=, P(11) = P(12) = %3D %3D O B. P(2) = P(3) = P(4) = P(5) = P(6) = P(7) = , P(8) = P(9) = P(10) =, P(11) = , P(12) = %3D
Extracted text: O C. P(3)= P(4) = P(5) = P(6) = P(7) = P(8) = P(9) = , P(10) = P(11) = %3D O D. P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = %3D Calculate the expected value of x. E(x) = (Type an integer or a decimal. Do not round.) b. Calculate the variance of x. o = (Simplify your answer.) c. Calculate the standard deviation of x. (Round to three decimal places as needed.) %3D