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The average of two identical uniform distributions Generate two sets of 1000 uniform random numbers between 0 and 1 in two columns of the Excel sheet for problem 2 (1 denote the random variables as x1 and x2). Add a third column in which you calculate the average of x1 and 2 (y = (x1+x2y2). 1. Construct the histograms for x1, x2, and y with the bins 0.1,0.2, ..., 0.9. Paste the histograms in the answer sheet. (6 pts) 2. What is the distribution of y? What is the mean and standard deviation of y? (4 pts) Modules 1 and 2.xlsx D G 01 Paste your x1 histogram here. Paste your x2 histogram hore. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 02 SS 56 57 58 59 60 61 Paste your Y histogram here What is the distribution of Y Type your answer here. Mean (Expected Value of Y Standard Deviation of Y B C D E F G 1x1 x2 3 A 1 Replication 2 3 4 5 6 7 8 9 10 5 7 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 The average of two identical uniform distributions Generate two sets of 1000 uniform random numbers between 0 and 1 in two columns of the Excel sheet for problem 2 (1 denote the random variables as x1 and x2). Add a third column in which you calculate the average of x1 and 2 (y = (x1+x2y2). 1. Construct the histograms for x1, x2, and y with the bins 0.1,0.2, ..., 0.9. Paste the histograms in the answer sheet. (6 pts) 2. What is the distribution of y? What is the mean and standard deviation of y? (4 pts) Modules 1 and 2.xlsx D G 01 Paste your x1 histogram here. Paste your x2 histogram hore. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 02 SS 56 57 58 59 60 61 Paste your Y histogram here What is the distribution of Y Type your answer here. Mean (Expected Value of Y Standard Deviation of Y B C D E F G 1x1 x2 3 A 1 Replication 2 3 4 5 6 7 8 9 10 5 7 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33