Two numbers are selected are random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the  probability distribution of X.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the Possible Values of X
We are selecting two numbers from the set {2, 3, 4, 5, 6, 7} without replacement. Let X denote the larger of the two numbers selected. The possible values of X can be determined as follows:

- The smallest pair that can be selected is (2, 3), which gives X = 3.
- The largest pair that can be selected is (6, 7), which gives X = 7.

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