For a random variable X, E(X)=3 and `E(X^2)=11` Then, variance of X is

Options

A. 8
B. 5
C. 2
D. 1

Explanation

To find the variance of the random variable \( X \), we can use the formula for variance:

\[ \text{Var}(X) = E(X^2) - (E(X))^2 \]

We are given the following values:
- \( E(X) = 3 \)
- \( E(X^2) = 11 \)

Now, let's calculate the variance step by step.

### Step 1: Calculate \( (E(X))^2 \)
First, we need to calculate \( (E(X))^2 \):

\[ (E(X))^2 = (3)^2 = 9 \]

### Step 2: Substitute the values into the variance formula
Now we substitute the values into the variance formula:

\[ \text{Var}(X) = E(X^2) - (E(X))^2 = 11 - 9 \]

### Step 3: Perform the subtraction
Now, we perform the subtraction:

\[ \text{Var}(X) = 11 - 9 = 2 \]

### Conclusion
The variance of the random variable \( X \) is:

\[ \text{Var}(X) = 2 \]