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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 the waiting time is more than 4 minutes.
Solution
Required probability P(X > 4)
= `int_(4)^∞ f (x)dx`
= `int_(4)^5 f (x)dx`+` int_(5)^∞ f (x)dx`
= `int_(4)^5 1/5 dx + 0`
= `1/5 int_(4)^5 1dx`
= `1/5[x]_4^5`
= `1/5 [5 - 4]`
= `1/5`
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