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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)
Solution
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)`.
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