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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 more than 4 minutes.

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#### Solution

Required probabilityP(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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