Question

For the following probability distribution, the standard deviation of the random variable X is

X	2	3	4
p(X=\(x\))	0.2	0.5	0.3

• A. \(0.5\)
• B. \(0.6\)
• C. \(0.61\)
• D. \(0.7\)

Hint:

Compute E(X) and E(X^2), then variance = E(X^2) - [E(X)]^2.

Answer 1

The Correct Option is D

Step 1: Using deviations
Mean is 3.1. Deviations: $-1.1, -0.1, 0.9$.

Step 2: Variance
$0.2(1.21) + 0.5(0.01) + 0.3(0.81) = 0.242 + 0.005 + 0.243 = 0.49$.

Step 3: SD
$\sqrt{0.49} = 0.7$. Option (D).

Final Answer:
Option (D). \[ \boxed{0.7} \]