Probability And Uniform Distribution

Step 1: Understand the probability density function (p.d.f.).
The p.d.f. is a uniform distribution between 0 and 5 minutes, with a constant value of over this interval. The total area under the curve must equal 1, which is true for a uniform distribution.

Step 2: Calculate the probability for part (i).
We are asked to find the probability that the waiting time is between 1 and 3 minutes. This is the integral of from to :

Step 3: Solve the integral for part (i).

Step 4: Calculate the probability for part (ii).
Next, we are asked to find the probability that the waiting time is more than 4 minutes. This is the integral of from to :

Step 5: Solve the integral for part (ii).
Final Answers: