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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(0.5 ≤ X ≤ 1.5)
Solution
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)`.
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