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.

Answer 1

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`