Three fair dice are thrown: the first die has faces with values 2, 2,2,3,3,3; the second...

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Three fair dice are thrown: the first die has faces with values 2, 2,2,3,3,3; the second die has faces with values 1,4,7, 10; and the third die has faces with values 3,3,3, 20. The product of the three die results is called P and the sum of the three die results is called S. (a) Calculate the expectation and variance of A = 6S – 3. (Justify any assumptions made in your calculations.) (b) Calculate the expectation and variance of B = 3P + 5. (Justify any assumptions made in your calculations.) Three fair dice are thrown: the first die has faces with values 2, 2,2,3,3,3; the second die has faces with values 1,4,7, 10; and the third die has faces with values 3,3,3, 20. The product of the three die results is called P and the sum of the three die results is called S. (a) Calculate the expectation and variance of A = 6S – 3. (Justify any assumptions made in your calculations.) (b) Calculate the expectation and variance of B = 3P + 5. (Justify any assumptions made in your calculations.)