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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 ≥ 1.5)
Solution
P(X ≥ 1.5) = `int_1.5^2 f(x)*dx`
= `0.5 int_1.5^2x*dx`
= `(0.5)/(2)[x^2]_1.5^2`
= `(1)/(4)[4 - 2.25]`
= `(1)/(4) xx (7)/(4)`
= `(7)/(16)`.
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