A random variable X is uniformly distributed on the interval [10, 30]. What is the variance Var(X)?
Answer and explanation
Correct answer: A. 100/3
- Step 1: For a continuous uniform distribution U(a, b), variance is Var(X) = (b - a)^2 / 12. Step 2. Here a = 10 and b = 30, so b - a = 20. Step 3. Compute: (20)^2 / 12 = 400 / 12 = 100 / 3. Answer: 100/3. Why not the others: 20/3 forgets to square (b - a); 50/3 divides by 24; 100 is standard deviation squared without the 1/12 factor.
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