Question

Wait times for a bus follow a uniform distribution over the interval 0 to 10 minutes. Determine the probability that a person will wait between 4.0 mi

Answer 1

P(x=4) = 0.4

Explanation:

The density function of a continuous r.v is called a uniform distribution when between the end points any two sub intervals of the same length containing X, have the same probability.

f(x)= 1/ b-a a≤ x≤ b

Here a = 0 and b= 10 but we want to know the probability of wait time between 4 minutes and 10 minutes

P (X=x) = (x-a) 1/(b-a)

P(x=4) = (4-0) 1/ 10-0

= 4/10= 0.4