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/3 62% Question 3: (6 points) Two six-sided blased dice [X&YI Second blased die M has the following probability distribution as above: In 1 0.3 Pyl 2 0.2 3 0.1 4 0.1 5 0.2 6 0.1 What is the mean, variance, and standard deviation of 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 difference between two dice and show the detail results. [use calculator only) b. Also, simulate the die tossing experiment for25 tossing for each die and calculate mean, variance, standard deviation of difference between two dice. Use only the randem numbers provided. 2 Calibri 11 B Av fx G B D Homework-3: Q3-- Simulation Prob. Cum Prob R# Dice # 1 2 3 4 5 6 Trial R# Dice1 # (x) Dice2 # (y) - 1 2 R# 2 8 3 4 5 1 1 9 4 13 0 1 6 7 8 7 4 3 100 wool 2 9 10 9 8 9 3 11 12 13 14 5 0 11 9 3 HW3 01 HW3_Q2 HW3_03 + calculation Mode: Automatic Workbock Statistics Home Insert Draw Page Layout Formulas Data Review View Help Calibri v 11 B Hav Av ... 29 fx A B D E F G H 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 8 9 3 9 7 1 1 1 8 2 7 7 6 0 8 8 8 5 0 1 3 9 1 7 5 3 2 4 7 3 5 9 + From column G: E(X-Y) = V{X-Y) COV(X,Y)= From column D: From column : E(X) - E(Y) = 1 Var(X) = Var(Y) = 2 Std X) - Std (Y) 3 Using Formula: 5 EX-Y) = -6 V (X-Y) 7 Std (X-Y) HW3 Q1 HW3 Q2 HW3_Q3 + Calculation Mode: Automatic Workbook Stadste g MacB /3 62% Question 3: (6 points) Two six-sided blased dice [X&YI Second blased die M has the following probability distribution as above: In 1 0.3 Pyl 2 0.2 3 0.1 4 0.1 5 0.2 6 0.1 What is the mean, variance, and standard deviation of 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 difference between two dice and show the detail results. [use calculator only) b. Also, simulate the die tossing experiment for25 tossing for each die and calculate mean, variance, standard deviation of difference between two dice. Use only the randem numbers provided. 2 Calibri 11 B Av fx G B D Homework-3: Q3-- Simulation Prob. Cum Prob R# Dice # 1 2 3 4 5 6 Trial R# Dice1 # (x) Dice2 # (y) - 1 2 R# 2 8 3 4 5 1 1 9 4 13 0 1 6 7 8 7 4 3 100 wool 2 9 10 9 8 9 3 11 12 13 14 5 0 11 9 3 HW3 01 HW3_Q2 HW3_03 + calculation Mode: Automatic Workbock Statistics Home Insert Draw Page Layout Formulas Data Review View Help Calibri v 11 B Hav Av ... 29 fx A B D E F G H 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 8 9 3 9 7 1 1 1 8 2 7 7 6 0 8 8 8 5 0 1 3 9 1 7 5 3 2 4 7 3 5 9 + From column G: E(X-Y) = V{X-Y) COV(X,Y)= From column D: From column : E(X) - E(Y) = 1 Var(X) = Var(Y) = 2 Std X) - Std (Y) 3 Using Formula: 5 EX-Y) = -6 V (X-Y) 7 Std (X-Y) HW3 Q1 HW3 Q2 HW3_Q3 + Calculation Mode: Automatic Workbook Stadste g MacB