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 of finding the mean and variance of the random variable \( X \), which denotes the larger of two numbers selected at random (without replacement) from the set of positive integers {2, 3, 4, 5, 6, 7}, we will follow these steps:

### Step 1: Determine the Sample Space
The total number of ways to choose 2 numbers from the set {2, 3, 4, 5, 6, 7} is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of items to choose from and \( r \) is the number of items to choose. Here, \( n = 6 \) and \( r = 2 \).

\[ \text{Total Sample Space} = \binom{6}{2} = 15 \]
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