Question

The p.d.f. of a random variable X is given by :
f(x) = 2x,                  0 ≤ x ≤ 1
      = 0,                    otherwise
Find `P(1/3 < x < 1/2)`

Answer 1

`p(1/3 < x < 1/2) = int_(1/2)^(1/3) f(x) dx`

= `int_(1/3)^(1/2) 2x dx`

= `[ 2(x^2/2)]_(1/3)^(1/2) = [(x^2)]_(1/3)^(1/2)`

= `(1/2)^2 - (1/3)^2`

= `1/4 - 1/9`

= `5/36`