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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(0.5 ≤ x ≤ 1.5)
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Solution
f(x) = 0.5 x , 0 ≤ x ≤ 2
= 0 , otherwise
P (0.5 ≤ X ≤ 1.5)
= `int_0.5^1.5 0.5 "x"`
`= 0.5 int_0.5^1.5 "x dx"`
`= 1/2 xx ["x"^2/2]_0.5^1.5`
`= 1/2 xx 1/2 [(1.5)^2 - (0.5)^2]`
`= 1/2 xx 1/2 [2.25 - 0.25]`
`= 1/4 xx 2 = 1/2`
P (0.5 ≤ X ≤ 1.5) = `1/2`
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