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A local caterer receives orders by telephone. The arrival of orders is modelled as a Poisson process, where the caterer receives on average of 3 orders per hour during its operating hours (11 am to 8 pm daily). No orders are accepted after hours. Use this information and answer the following questions.

Question 18 Question c: The caterer just received an order. What is the probability that it does not receive any orders in the next 30 minutes? (Use four decimal places) Question 19 Question 20 Question d: It has been 10 minutes since the last catering order was placed. What is the probability that the next order is placed at least 28 minutes after the last one? (Use four decimal places) Question e: In order to calculate the probability that no order has been placed for an hour, you define the following random variables and their distribution: 5 pts X-time between two orders (in hours), X-expon(3) Y = number of orders placed in an hour, Y- Poisson(3) What is the correct method to calculate the probability that no order has been placed for an hour? (select all that apply) □PX>1) ORY-0) OP(X=0)) P(X= 1)) OPY-1) PY 1) 5 pts 5 pts Text