Question
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
Solution
Since 1 cannot be greater than the other selected number.
∴ X can take values 2, 3, 4, 5, 6.
∴ P(X = 2) = P(2 and a number less than 2 are selected)
= P(1 and 2 are selected)
P(X = 3) = P(3 and a number less than 3 are selected)
[∵ (1, 3) and (2, 3) can be selected]
P(X = 4) = P(4 and a number less than 4 are selected)
[∵ (1, 4), (2, 4) and (3, 4) can be selected]
P(X = 5) = P(5 and a number less than 5 are selected)
[∵ (1, 5), (2, 5), (3, 5) and (4, 5) can be selected]
P(X = 6) = P(6 and a number less than 6 are selected)
[∵ (1, 6), (2, 6), (3, 6), (4, 6) and (5, 6) can be selected]
∴ probability distribution table is
Expectation of X = E(X) = 
