solving exercises
نویسندگان
چکیده
(a) Consider a random assignment α where every variable is set independently and with probability 12 to either 0 or 1. The probability that a 3-clause is not satis ed by α is 1 8 , which is the case when all its literals evaluate to zero. Therefore, the probability that a clause is satis ed is 1− 18 = 7 8 . Let Xi be the indicator variable for the event that clause i is satis ed by the random assignment. We have seen that E[Xi] = 7 8 for all i = 1, . . . ,m. By linearity of expectation we get
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