A branch of a certain bank in New York City has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows. Calculate the following probabilities directly form the cdf: (i) p(2), that is, P(X = 2); (ii) P(X > 3); (iii) P (2 ≤ X ≤ 5); (iv) P(2 < X < 5).               0        x < 0               0.06   0 ≤ x < 1               0.19   1 ≤ x < 2 F(x) = {  0.39   2 ≤ x < 3               0.67   3 ≤ x < 4               0.92   4 ≤ x < 5               0.97   5 ≤ x < 6               1         6 ≤ x

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A branch of a certain bank in New York City has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows. Calculate the following probabilities directly form the cdf: (i) p(2), that is, P(X = 2); (ii) P(X > 3); (iii) P (2 ≤ X ≤ 5); (iv) P(2 < X < 5).
              0        x < 0
              0.06   0 ≤ x < 1
              0.19   1 ≤ x < 2
F(x) = {  0.39   2 ≤ x < 3
              0.67   3 ≤ x < 4
              0.92   4 ≤ x < 5
              0.97   5 ≤ x < 6
              1         6 ≤ x

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