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Question
Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by
f(x) = `{(1/5, "for" 0 ≤ x ≤ 5),(0, "otherwise".):}`
Find the probability that waiting time is more than 4 minutes.
Solution
P(waiting time is more than 4 minutes)
= P(X > 4) = `int_4^5 f(x)*dx`
= `int_4^5 (1)/(5)*dx`
= `(1)/(5) int_4^5 1*dx`
= `(1)/(5)[x]_4^5`
= `(1)/(5)[5 - 4]`
= `(1)/(5)`.
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