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Question
Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f
f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise. Calculate: P(x ≥ 1.5)
Solution
f(x) = 0.5 x , 0 ≤ x ≤ 2
= 0 , otherwise
P(x ≥ 1.5)
= `int_(1.5)^2 f(x) dx`
= `int_(1.5)^2 0.5x dx`
= ` 0.5[x^2/2]_(1.5)^2`
= `0.5[4/2 - 2.25/2]`
= `0.5 xx 1.75/2`
= `0.875/2`
= `0.875/2 xx 1000/1000`
= `(875 ÷ 125)/(2000 ÷ 125)`
= `7/16`
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