# Suppose that X is waiting time in minutes for a bus and its p.d.f. is given by f (x) = 15 , for 0 ≤ x ≤ 5 and = 0 otherwise. Find the probability that waiting time is more than 4 minutes. - Mathematics and Statistics

Sum

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 waiting time is more than 4 minutes.

#### Solution

Required probabilityP(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

Concept: Probability Distribution of Discrete Random Variables
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