Question 4 (15 marks) Suppose calls to a software support centre over a given period of time occur randomly, independently and at a homogeneous rate of A calls per hour. In solving for the questions below set 11 =last digit of your student number + 10, for example if your student number is 20327203 then the last digit is 3 and l = 10 + 3 = 13 calls per hour. Note: in this question I ask you to use R to solve for probabilities. To get full marks you need to include the probability expression in terms of the random variable, as well as its simplication and then the probability value obtained from R. For example, if you are asked to solve for the probability that we observe less than 2 calls in an hour your solution should include the following: P(X ppois (1,13) [l] 3.164461e-05 a) (2) In this question we are assuming that the average number of calls received is homogenous i.e the same regardless of the time of day or day of week etc. Explain, in your own words, whether this assumption is valid. a) (2) Use R to solve for the probability that there are less than 4 calls in a 30-minute period. b) (2) Use R to solve for the probability that there are at least 10 calls received in a 1-hour period. c) (2) Use R to solve for the probability that exactly 25 calls are received in a two-hour interval. d) (2) The support centre would like to track the volume of calls. If in a two-hour interval more than 35 calls are received the support centre calls this a \"stressful event\". Use R to solve for the probability that in any particular two-hour interval a \"stressful event\" occurs. e) (3) Assume that the day is considered to run om 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. Use R to solve for the probability that among the 6 two-hour intervals less than 2 are labeled as \"stressful event\". 1) (2) Assume that the day is considered to run from 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. In addition, assume that the support centre is open Monday to Friday each week. Assuming we just started a new week i.e Monday at 8am, use R to solve for the probability that the rst \"stressful event\" occurs after the 12th two-hour interval that passes