ALL ABOUT STATISTICAL THEORY

. Incoming telephone calls to a school arrive at random times. The average rate will vary according to the day of the week. On Monday mornings, in term time there is a constant average rate of 4 per hour. What is the probability of receiving (a) [3 points} 6 or more calls in a particular hour? (12-) (5 points} 3 or fewer calls in a particular period of two home? {9) [5 points) During term time on Friday afternoon the average rate is also constant and it is observed that the probability of no calls being received during a. particular hour is 0.202. What is the average rate of calls on Friday afternoon? . Let X and Y be jointly continuous with joint pdf fxrll'a a) = (\"=2 + 1:)I[0,1}{Ilf{,2}[yl- {a} [4 points] Find c. {b} [5 points] Find the marginal pdf's of X and Y. {c} [4 points) Find PIX + Y :_-" 1]. . The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 3 minutes. (a) (4 points] Find the probability that the time interval between two successive barges is less than 5 minutes. [is] (4 points] Find a. time interval t such that we can be 95% sure that the time interval between two successive 1Merges will be greater than t