Customers call a customer service telephone line at an average rate of 20 calls per hour.

(a) What is the expected amount of time one would need to wait for the first call of the day? Write down the reason behind your answer.

(b) What is the expected amount of time one would need to wait for the tenth call of the day? Write down the reason behind your answer. [Hint: Use the memorylessness property.]

(c) Compute the variance of the amount of time one would need to wait for the first call of the day. Note: You may need to do integration-by-parts twice. You are NOT allowed to use a formula and write that in as your answer - you must compute it