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

Answer 1

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^2]_1^3`

= `(1)/(5)[3 - 1]`

= `(2)/(5)`.