There are 5 cards numbered 1 to 5 , one number on one card . Two cards are drawn at random without replacement . Let X denotes the sum of the numbers on two cards drawn . Find the mean and variance of X.

Explanation

To solve the problem step by step, we will first identify the sample space, then calculate the probabilities for each possible value of X (the sum of the numbers on the two drawn cards), and finally compute the mean and variance of X.

### Step 1: Identify the Sample Space
We have 5 cards numbered from 1 to 5. When drawing two cards without replacement, the possible pairs of cards (in ordered pairs) are:

- (1, 2), (1, 3), (1, 4), (1, 5)
- (2, 1), (2, 3), (2, 4), (2, 5)
- (3, 1), (3, 2), (3, 4), (3, 5)
...