Hi! Please provide the workings along with the answers for the questions below. Thank you

NANYANG TECHNOLOGICAL UNIVERSITY SPMS/DIVISION OF MATHEMATICAL SCIENCES 2021/22 Semester 1 MH2814 Probability and Statistics Tutorial 3 For the tutorial in Week 4 (30 August73 September), let us discu I EX. 2.96, 2.100, 2.102, 3.10, 3.11, 3.12, 3.26. Ex. 2.96. Police plan to enforce speed limits by using radar traps at four dierent locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that she will receive a speeding ticket? (Assume that a person who is speeding will speed will only pass through exactly one of these four locations. The qumtion should mentioned this explicit.) [Answerz [127.] Ex. 2.100. A regional telephone company operates three identical relay stations at different locations. During a one-year period, the number of malfunctions reported by each station and the causm are shown below. Station Problems with electricity supplied Computer malfunction Malfunctioning electrical equipment Caused by other human error Nolan; outm mMMD'Q Suppose that a malfunction was reported and it was found to be caused by other human errors. What is the probability that it came from station C? [Answerz [12632.] Ex. 2.102. Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opens a door, say B, and showed there was no prize behind it. Now the host offers you the option of either staying at the door that you picked (A) or switching to the remaining unopened door (C). Using probability to explain whether you should switch or not. Ex. 3.10. Find a formula for the probability distribution of the random variable X repre- senting the outcome where a number is drawn at random from a list of integers from [I to 9, both inclusive. 2 Ex. 3.11. A shipment of 7 televisions contains '2 defective ones. A hotel makes a random purchase of 3 televisions. If I is the number of defective ones purchased by the hotel, nd the probability distribution of X. Express the results graphically as a probability histogram. Ex. 3.12. An investment rm otters its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a randomly selected bond is 0, MI; i. Isma; F(t)= %, 35t 3); (c) P(1.4