Topic: Engineering Mathematics
Let X have the probability density function f(x) = (3/4)*(1-x²) if -1 <= x <= 1, and 0 otherwise. P(-1/2 <= x <= 1/2) is
- A. 68.75%
- B. 31.36%
- C. 95%
- D. 60.7%
Answer: A. 68.75%
Explanation: P(-1/2 <= x <= 1/2) = Integral from -1/2 to 1/2 of (3/4)*(1 - x²) dx. Solving this: (3/4) * [x - x³/3] evaluated from -1/2 to 1/2. = (3/4) * [(1/2 - 1/24) - (-1/2 + 1/24)] = (3/4) * [11/12] = 11/16 = 68.75%.