Variance

To find the variance of the number obtained in a throw of an unbiased die, we will follow these steps:

1. An unbiased die has 6 faces with numbers 1 to 6. Each number has an equal probability of appearing, which is .

2. The expected value of the numbers rolled can be calculated using the formula:

3. Calculating the above gives:

4. The variance is calculated using the formula:

5. First, calculate :

6. Calculating the above gives:

7. Substitute the values into the variance formula:

8. Calculate , then:

9. Simplifying :

Therefore, the correct variance is .