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 the probability distribution of the random variable X, and hence find the mean of the distribution.
If 1 is the smallest number,
the other numbers are:2,3,4,5,6
If 2 is the smallest number, the other numbers are:3,4,5,6
If 3 is the smallest number, the other numbers are:4,5,6
If 4 is the smallest number, the other numbers are: 5, 6
If 5 is the smallest number, the other number is:6
Thus, there are 15 set of numbers in the sample space.
Let X be
X: 2 3 4 5 6
1/15 2/15 3/15 4/15 5/15
We know that,
