Two numbers are selected at random, without replacement from the first 6 positive integers. Let X denote the larger of the two numbers. Then E ( X )=

Step-by-step solution

Two numbers are selected without replacement from the set S = 1, 2, 3, 4, 5, 6 . The total number of possible pairs is 6 2 = 15 . Let X denote the larger of the two numbers selected. The probability that X = k is the number of pairs where k is the maximum, divided by 15. For k = 2, 3, 4, 5, 6 , there are k - 1 such pairs, so P(X = k) = k - 1 15 . The expected value is computed as E(X) = _ k=2 ⁶ k k - 1 15 = 1 15 _ k=2 ⁶ (k^2 - k) . Evaluating the sum: 2^2 - 2 + 3^2 - 3 + 4^2 - 4 + 5^2 - 5 + 6^2 - 6 = (4 - 2) + (9 -