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.

Answer 1

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)`.