For a random variable X, if Var (X) = 4 and `E(X^(2))=13`, the value of E(X) is

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the value of \( E(X) \) given that \( \text{Var}(X) = 4 \) and \( E(X^2) = 13 \), we can use the relationship between variance, expected value, and the expected value of the square of a random variable.

### Step-by-Step Solution:

1. **Recall the formula for variance**:
The variance of a random variable \( X \) is given by the formula:
\[ \text{Var}(X) = E(X^2) - (E(X))^2 \]

2. **Substitute the known values into the formula**:
We know that \( \text{Var}(X) = 4 \) and \( E(X^2) = 13 \). Plugging these values into the variance formula gives:
\[ 4 = 13 - (E(X))^2 \]

3. **Rearrange the equation to solve for \( (E(X))^2 \)**:
Rearranging the equation, we get:
\[ (E(X))^2 = 13 - 4 \]
\[ (E(X))^2 = 9 \]

4. **Take the square root to find \( E(X) \)**:
To find \( E(X) \), take the square root of both sides:
\[ E(X) = \sqrt{9} \]
\[ E(X) = 3 \]

Thus, the value of \( E(X) \) is \( 3 \).