Question

Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

Calculate: P(x≤1)

Answer 1

f(x) = 0.5 x ,      0 ≤ x ≤ 2

      = 0 ,           otherwise

P (X ≤ 1) = `int_0^1 0.5  "x dx"`

`= 0.5 int_0^1 "x  dx"`

`= 0.5 ["x"^2/2]_0^1`

`= 1/2 xx 1/2 = 1/4`

∴ P (X ≤ 1) = `1/4`