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

Answer

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

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

### Step 1: Identify the given values
We are given:
- \( E(X) = 3 \)
- \( E(X^2) = 11 \)

### Step 2: Calculate \( (E(X))^2 \)
Now, we need to calculate \( (E(X))^2 \):
\[ (E(X))^2 = (3)^2 = 9 \]

### Step 3: Substitute values into the variance formula
Now we can substitute the values into the variance formula:
\[ \text{Variance}(X) = E(X^2) - (E(X))^2 = 11 - 9 \]

### Step 4: Perform the subtraction
Now, perform the subtraction:
\[ \text{Variance}(X) = 11 - 9 = 2 \]

### Conclusion
Thus, the variance of \( X \) is:
\[ \text{Variance}(X) = 2 \]

### Final Answer
The variance of \( X \) is \( 2 \).

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