Let X be a continuous random variable with p.d.f: f(x) = ax, 0 < x ≤ 1, f(x) = a, 1 ≤ x ≤ 2, f(x) = -ax + 3a, 2 ≤ x ≤ 3

Question

Let X be a continuous random variable with p.d.f: 

\(f(x) = \begin{cases} ax,&0<x≤1\\ a,&1≤x≤2\\ -ax + 3a, &2≤x≤3 \\0,& otherwise\end{cases}\)

(i) Find ‘a’ 

(ii) compute P(X ≤ 1.5)

Answer 1

Since f(x) is p.d.f \(\int\limits_{-∞}^{∞}\)f(x) dx = 1