Please use the excel format to answer the question.

Question 3: (6 points) Two six-sided biased dice [X & Y] The second biased die [V] has the following probability distribution as above: 2 5 6 y Ply) 1 0.3 3 0.1 0.2 4 0.1 0.2 0.1 What are the mean, variance, and standard deviation of the difference between two dice (x-y) tossing both for a. and b. below, assuming X and Y are independent? a. Calculate the theoretical values of mean, variance, standard deviation of the difference between two dice and show the detailed results. (use calculator only] b. Also, simulate the die tossing experiment for25 tossing for each die and calculate mean, variance, the standard deviation of the difference between two dice. Use only the random numbers provided. A F G B D Homework-3: Q3--Simulation 1 2 Prob. Cum ProbR# Dice # 1 4 2 5 6 7 3 4 oc 5 6 R# Dice1 #(x) R# Dice2 # (y) X-Y Trial 1 2 1 2 1 8 9 O 9 10 11 12 13 14 15 16 17 18 19 20 21 22 3 4 4 1 5 3 4 7 0 6 7 8 4 1 3 6 9 9 3 ool w 10 8 8 A B D E F G H 9 5 11 12 3 0 13 9 1 14 7 3 15 1 9 16 1 1 17 1 7 18 8 5 19 1918 2 3 20 7 2 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 21 7 4 22 6 7 23 0 3 24 8 5 25 8 9 = From column D: E(X) Var(x) = Std(X) = From column F: E(Y) Var(Y) = Std (Y) = From column G: E(X-Y) V(X-Y) - COV(X,Y)= = 44 Using Formula: A 44 45 46 47 B B Using Formula: E(X-Y) = v (X-Y) - Std (X - Y)=