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Find the expected value, ì, for the sum of two fair dice. The probability distribution for the sum of two dice is given in the table. ì = 1
2=1/36, 3=2/36, 4=3/36, 5=4/36, 6=5/36, 7=6/36, 8=5/36, 9=4/36, 10=3/36, 11=2/36, 12=1/36
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The expected value, ì, is calculated by taking the sum of all possible outcomes multiplied by their corresponding probabilities. ì = (1)(1/36) + (2)(2/36) + (3)(3/36) + (4)(4/36) + (5)(5/36) + (6)(6/36) + (7)(5/36) + (8)(4/36) + (9)(3/36) + (10)(2/36) + (11)(1/36) ì = 36/36 = 1 Therefore, the expected value for the sum of two fair dice is 1.
