Random Variables And Its Probability Distributions

1. Understand the probability distribution:

The random variable has the following probability distribution:

2. Find the value of :

Since the total probability must sum to 1:

3. Verify the mean condition:

The mean is given by:

This matches the given mean.

4. Calculate the variance:

First, compute :

Then, the variance is:

5. Match the result to the options:

The variance corresponds to option (B).

Correct Answer: (B)