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 ≥ 1.5)

Answer 1

f(x) = 0.5 x ,      0 ≤ x ≤ 2

      = 0 ,            otherwise

P(x ≥ 1.5)

= `int_(1.5)^2 f(x) dx`

= `int_(1.5)^2 0.5x dx`

= ` 0.5[x^2/2]_(1.5)^2`

= `0.5[4/2 - 2.25/2]`

= `0.5 xx 1.75/2`

= `0.875/2`

= `0.875/2 xx 1000/1000`

= `(875 ÷ 125)/(2000  ÷ 125)`

= `7/16`