For the random variable X , if V(X) = 4 , E(X) = 3 , then `E(X^(2))` is …

Options

A. 9
B. 13
C. 12
D. 7

Answer

To find \( E(X^2) \) given that \( V(X) = 4 \) and \( E(X) = 3 \), we can use the relationship between variance, expected value, and the expected value of the square of a random variable. The formula we will use is:

\[ V(X) = E(X^2) - (E(X))^2 \]

### Step-by-Step Solution:

1. **Write Down Given Values**:
- Variance \( V(X) = 4 \)
- Expected value \( E(X) = 3 \)

2. **Substitute into the Variance Formula**:
\[ V(X) = E(X^2) - (E(X))^2 \]
Substituting the known values:
\[ 4 = E(X^2) - (3)^2 \]

3. **Calculate \( (E(X))^2 \)**:
\[ (E(X))^2 = 3^2 = 9 \]

4. **Rewrite the Equation**:
Substitute \( (E(X))^2 \) back into the equation:
\[ 4 = E(X^2) - 9 \]

5. **Solve for \( E(X^2) \)**:
Rearranging the equation gives:
\[ E(X^2) = 4 + 9 \]
\[ E(X^2) = 13 \]

### Final Answer:
\[ E(X^2) = 13 \]

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