Paper 2 · November 2022 · Continuous Random Variables
A continuous random variable X has probability density function f(x) = (3/8)x^2 for 0 <= x <= 2. What is the cumulative distribution function F(x) for 0 <= x <= 2?
AF(x) = x^2/8
BF(x) = 3x^2/8
CF(x) = x^3/6
DF(x) = x^3/8
Explanation
F(x) is the integral of f(t) from 0 to x: the integral of (3/8)t^2 dt = (3/8)(x^3/3) = x^3/8. Differentiating instead of integrating gives x^2/8 or 3x^2/8, and dividing by the wrong constant gives x^3/6.
Derived from ZIMSEC Statistics Paper 2, November 2022, Q3