A continuous random variable X has probability density function f(x) = dfrac38x^2 for 0 ≤ x ≤ 2. Find the value of the cumulative distribution function F(1).

A continuous random variable X has probability density function $f(x) = \dfrac{3}{8}x^2$ for $0 \leq x \leq 2$ . Find the value of the cumulative distribution function $F(1)$ .

Model answer

0.125

Also accepted: 1/8

Explanation

F(x) = the integral of (3/8)t^2 from 0 to x = x^3/8. So F(1) = 1^3/8 = 0.125.

Derived from ZIMSEC Statistics Paper 1, November 2022, Q3

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