Question

If \(X\) follows a uniform distribution on \([0, 1]\), then the variance of \(X\) is:

• A. 1
• B. 0
• C. 1/12
• D. 1/2

Hint:

Exam Tip:
For uniform distribution:
• Mean \(= \frac{a + b}{2}\).
• Variance \(= \frac{(b - a)^2}{12}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The uniform distribution on \([a, b]\) has constant probability density function.
For \(X \sim U(a, b)\), the variance is given by: \[ \text{Var}(X) = \frac{(b - a)^2}{12} \]

Step 2: Key Formula or Approach:
Here, \(a = 0\), \(b = 1\).
So, \[ \text{Var}(X) = \frac{(1 - 0)^2}{12} = \frac{1}{12} \]

Step 3: Detailed Explanation:
The mean of \(U(0, 1)\) is \(1/2\).
Using the formula for variance, we get \(1/12\).

Step 4: Final Answer:
Therefore, option (C) is correct.