Question

The probability distribution of a random variable X is given by

Then the variance of X is

• A. 1.76
• B. 2.45
• C. 1.56
• D. 4.8

Hint:

$Var(X) = E(X^2) - \mu^2$.

Answer 1

The Correct Option is C

Step 1: Calculate Mean \(E(X)\)
$E(X) = \sum x_i P_i = (-2)(0.2) + (-1)(0.1) + 0 + (1)(0.3) + (2)(0.1)$
$E(X) = -0.4 - 0.1 + 0.3 + 0.2 = 0$.
Step 2: Calculate \(E(X^2)\)
$E(X^2) = \sum x_i^2 P_i = (4)(0.2) + (1)(0.1) + 0 + (1)(0.3) + (4)(0.1)$
$E(X^2) = 0.8 + 0.1 + 0.3 + 0.4 = 1.6$.
Step 3: Find Variance
$Var(X) = E(X^2) - [E(X)]^2 = 1.6 - 0^2 = 1.6$.
Step 4: Conclusion
Closest option is 1.56 (Possible typo in question distribution values). Based on standard calculations, it is 1.6.
Final Answer:(C)