Question

Given p.d.f. of a continuous random variable X is

`f(x) = x/8`, for 0 < x < 4

= 0, otherwise.

Then P(1 < X < 2) = ...........

Answer 1

Given:

`f(x) = x/8, 0<x<4`

`P(1<x<2) = int_1^2 x/8 dx`

`int x/8 dx = 1/8.x^2/2 = x^2/16`

`P(1<x<2) = [x^2/16]_1^2`

`= 4/16-1/16`

`= 3/16`