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Question
Suppose that X is waiting time in minutes for a bus and its p.d.f. is given by f(x) = `1/5`, for 0 ≤ x ≤ 5 and = 0 otherwise.
Find the probability that waiting time is between 1 and 3.
Solution
Required probability P(1 < X < 3)
= `int_(1)^3 f(x) dx`
= `int_(1)^3 1/5 (x) dx`
= `int_(1)^3 1/5 1 dx`
= `1/5 [x]_1^3`
= `1/5 [3 - 1]`
= `2/5`
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