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(X ≤ 1)

Answer 1

P(X ≤ 1) = `int_0^1 f(x)*dx`

= `int_0^1 0.5x*dx`

= `0.5 int_0^2*dx`

= `(0.5)/(2)[x^2]_0^1`

= `(1)/(4)[1 - 0]`

= `(1)/(4)`.