Question
Two the numbers are selected at random (without replacement) from first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of X. Find the mean and variance of this distribution.
Solution
First six positive integers are {1, 2, 3, 4, 5, 6}
No. of ways of selecting 2 numbers from 6 numbers without replacement = 
X denotes the larger of the two numbers, so X can take the values 2, 3, 4, 5, 6.
Probability distribution of X:
| X | 2 | 3 | 4 | 5 | 6 |
| P(x) | 1/15 | 2/15 | 3/15 | 4/15 | 5/15 |
Computation of Mean and Variance:
| xi | P(X=xi) |  |
 |
| 2 | 1/15 | 2/15 | 4/15 |
| 3 | 2/15 | 6/15 | 18/15 |
| 4 | 3/15 | 12/15 | 48/15 |
| 5 | 4/15 | 20/15 | 100/15 |
| 6 | 5/15 | 30/15 | 180/15 |
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