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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 between 1 and 3 minutes.
Solution
P (waiting time is between 1 and 3 minutes)
P(1 < X < 3) = `int_1^3 f(x)*dx`
= `int_1^3 (1)/(5)*dx`
= `(1)/(5) int_1^3 1*dx`
= `(1)/(5)[x]_1^3`
= `(1)/(5)[3 - 1]`
= `(2)/(5)`
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