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- Please solve the following problem. Quiz = Pass Quiz = Fail AI = Fail 0.1 0.2 AI = Pass 0.6 0.1 Mid = Pass Mid = Fail AI = Fail 0.2 0.2 AI = Pass 0.5 0.1 Suppose you have three events AI Grade, Quiz, and Mid. Here each event has two possible outcomes, either pass or fail. Additionally, given that AI Grade is observed, Quiz and Mid become independent of each other. Also, out of every 100 students, 30 students fail the AI course. Now, using the joint probability tables given, calculate P(AI Grade=Pass, Quiz=Fail, Mid=Fail).that range from 1 to 8 minutes apart. Assuming that the inter-arrival times are integer-valued with each of the 8 values having equal probability, following uniform distribution. The service times vary from 1 to 6 minutes (integer) with the probabilities given in the following table: Service time (in mins) Probability 1 0.10 2 0.20 3 0.30 4 0.25 5 0.10 6 0.05 The random numbers for inter-arrival time are: 913, 727, 015, 948, 309, 922, 753, 235, 302. The random numbers for service time are: 84, 10, 74, 53, 17, 79, 91, 67, 89, 38. As a student of AIT, use your knowledge in computer simulation and help Mr. Owusu to: a) Simulate the system for 10 customers and compute waiting time of customers, total time spent by a customer in the system and idle time of the server. b) i. Explain average waiting time and compute it ii. Explain average time spent in the system and compute it. c) i. Evaluate the probability of idle server ii.…(Please Solve problem by using your hand calculation and R). Suppose that X is the downloading time a movie, which follows a uniform distribution between 16 and 22 minutes. Let’s assume you want to download a movie. What is the probability that the download time will be (a) Less than 19 minutes? (b) More than 23 minutes? (c) Between 20 and 22 minutes? (d) What are the mean and standard deviation of the download times?
- 4It has been observed by management that some faculty member at the university demonstratesa lackadaisical attitude toward teaching. They seldom go to class yet at the end of each month they receive full salary. Management hasdecided that GHs200, 300, 400, and 500 will be deducted from a faculty’s salary if he/she offends once, twice, third time and forth time respectively in a month. This means that if a faculty member offends once in a month GHs200 will be deducted, if a faculty member offends twice in a month,GHs500 (i.e. 200+300) will be deducted, if a faculty member offends three times in a month GHs900(i.e. 200+300+400), will be deducted and if a faculty member offends four times in a month GHs1,400 (i.e. 200+300+400+500). Assuming all faculty members are ona flat salary rate of GHs 2000.a.Write a program to request for the names of four faculty members and number times he/she has absented him/herself from class. One of them should have absented him/herself once, another twice,…Consider two defaultable 1-year loans with a principal of $1 million each. The probability of default on each loan is 2.5%. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ ? million is 1 − ?. If a loan does not default, it yields a profit equal to $20,000. Compute the 1-year 98% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan.Consider values shown in the table below:i=1 (cold) i=2 (allergy) i=3 (stomach pain) p(Hi)0.60.30.1 p(E1 |Hi)0.30.80.3 p(E2 |Hi)0.60.90.0Those values represent (hypothetically) three mutually exclusive and exhaustive hypotheses for the patient’s condition. For example, H1: the patient has a cold, H2: the patient has an allergy, and H3: the patient has stomach pain with their prior probabilities, p(Hi)’s and two conditionally independent pieces of evidence (E1, patient sneezes and E2, patient coughs) which support these hypotheses to differing degrees. Therefore;a) Compute the posterior probabilities for the hypothesis if the patient sneezes. What is the conclusion that can be derived from this condition?b) Based on the answer from the previous result, as the patient coughs are now observed, compute the posterior probabilities for this condition. Explain the results.
- Star-crossed soap-opera lovers Noah and Julia have hada big argument. Julia’s sister Maria wants Noah and Julia tomake up, so she has told them both to go to the romanticgazebo at 1 P.M. Unfortunately, Noah and Julia are notpunctual. Each is equally likely to show up at the gazeboany time between 1 and 2 P.M. Assuming that each will stayfor 20 minutes, what is the probability that they will meet?You can model the arrival of each person using aRISKUNIFORM random variable. For example,RISKUNIFORM(1,2) is equally likely to choose any numberbetween 1 and 2 (including the endpoints 1 and 2).L. Brown, a direct marketer of women’s clothing, must determine how many telephone operators to schedule during each part of the day. W. L. Brown estimates that the number of phone calls received each hour of a typical eight-hour shift can be described by a discrete probability distribution in the excel template file. Each operator can handle 15 calls per hour and costs the company $20 per hour. Each phone call that is not handled is assumed to cost the company $6 in lost profit. Considering the options of employing 6, 8, 10, 12, 14, or 16 operators, use simulation to determine the number of operators that minimizes the expected hourly cost (labor costs plus lost profits).Melissa's null hypothesis is that the average calories in frozen Mac n Cheese is 350 (that is, the population average is 350). Since she only has one sample, she uses the bootstrap to estimate the average and ultimately decides to create a confidence interval. She also chooses an 8% p-value cutoff. What kind of confidence interval should she use? Melissa's null hypothesis is that the average calories in frozen Mac n Cheese is 350 (that is, the population average is 350). Since she only has one sample, she uses the bootstrap to estimate the average and ultimately decides to create a confidence interval. She also chooses an 8% p-value cutoff. What kind of confidence interval should she use? 95% 92% 8% Not enough information
- modeling and simulation question The mean time between arrivals of customers in a bank is 4 minutes. If a customer has already arrived in the bank,a) What is the probability that the next arrival will come after 5 minutes, if it follows exponential distribution?b) What is the probability that 6 customers will arrive in one-hour interval, if it follows Poisson distribution?II) Assume that the inter-arrival time is Poisson process distributed with a mean of 10 per hour and the service time has the exponential distribution with one customer every 5 minutes, and the system operates 8 hours a day. Assume you have M/M/1 queuing model, find(a) The utilization of the system.(b) The expected number in the queue.(c) The average waits in the queue.(d) The average waits in the system.(e) The number in the system.(f) The average cost per day from waiting if you assume the cost is JD10 for each hour lost by acustomer waiting.Suppose that a factory has two machines, Machine A and Machine B, both producing Phone touch screens. 40% of their touch screens come from Machine A and 60% of their touch screens come from Machine B. 10% of the touch screens produced by Machine A are defective and 5% of the touch screens from Machine B are defective. If randomly touch screen has been chosen and it is defective, what is the probability that it came from machine A? (Show your work)It has been observed by management that some faculty members at theuniversity demonstrate a lackadaisical attitude toward teaching. They seldom go to class yet at the end of each month they receive full salary. Management has decided that GHs 200, 300, 400, and 500 will be deducted from a faculty’s salary if he/she offends once, twice, third time and forth time respectively in a month. This means that if a faculty member offends once in a month GHs200 will be deducted, if a faculty member offends twice in a month, GHs 500 (i.e. 200+300) will be deducted, if a faculty member offends three times in a month GHs 900 (i.e. 200+300+400), will be deducted and if a faculty member offends four times in a month GHs 1,400 (i.e. 200+300+400+500). Assuming all faculty members are on a flat salary rate of GHs 2000.a. Write a program to request for the names of four faculty members and number times he/she has absented him/herself from class in a month.One of them should have absented him/herself…