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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.9 : In the modelling of the total of n rolls of a dice by an engineering student, let D be the random outcome of rolling a dice once. (a) Find the probability of outcome of D = 1, 2, 3, 4, 5 and 6. (b) Find the average score of each rolling of a dice D. (c) Find the expected value, Sn of n rolls of a dice in term of n and D. A new dice has a value of D* = D - 3.5. (d) Find the values of D* for each volume of D = 1, 2, 3, 4, 5 and 6. (e) Find the equivalent model of Sn in term of n and D. (f) Find the expected value of D*.
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Answer Posted / kangchuentat
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.9 : (a) P (1) = P (2) = P (3) = P (4) = P (5) = P (6) = 1 / 6. (b) Average score of D = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. (c) Expected value Sn = n (average score) = 3.5 n. (d) D* (D = 1) = 1 - 3.5 = - 2.5, D* (D = 2) = 2 - 3.5 = - 1.5, D* (D = 3) = 3 - 3.5 = - 0.5, D* (D = 4) = 4 - 3.5 = 0.5, D* (D = 5) = 5 - 3.5 = 1.5, D* (D = 6) = 6 - 3.5 = 2.5. (e) Sn = 3.5 n + nD*. (f) Expected value of D* = average of D* = [ D* (D = 1) + D* (D = 2) + D* (D = 3) + D* (D = 4) + D* (D = 5) + D* (D = 6) ] / 6 = (- 2.5 - 1.5 - 0.5 + 0.5 + 1.5 + 2.5) / 6 = 0. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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