Question

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

f(x) = `{(0.5x, "for" 0 ≤ x ≤ 2),(0, "otherwise".):}`
Calculate : P(0.5 ≤ X ≤ 1.5)

Answer 1

P(0.5 ≤ X ≤ 1.5) = `int_0.5^1.5 f(x)*dx`

= `0.5 int_0.5^1.5x*dx`

= `(0.5)/(2)[x^2]_0.5^1.5`

= `(1)/(4)[2.25 - 0.25]`

= `(1)/(4) xx 2`

= `(1)/(2)`.