4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate A; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.
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- What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 16.1 22.7 25.3 1.98 32.2 38.3 51.3 20.5 y 2.78 1.88 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex, Ey", Exy, and r. (Round r to three decimal places.) Ex= Ey= Ey? - Exy = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) critical t= Conclusion O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient evidence that p < 0. Reject the null hypothesis.…What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.x 12.1 26.3 32.2 38.3 51.3 20.5 22.7y 2.48 2.18 1.48 1.03 0.75 2.38 2.20 a) Find the predicted optimal time in hours for a dive depth of x = 22 meters. (Round your answer to two decimal places.)______ hr b) Find an 80% confidence interval for y when x = 22 meters. (Round your answers to two decimal places.)lower limit= ____ hrupper limit =____hr c) Find a 90% confidence interval for ? and interpret its meaning. (Round your answers to three decimal places.)lower limit =upper limit=Suppose the log-ins to a company's computer network follow a Poisson process with an average of three counts per minute. What is the mean time between counts? What is the standard deviation of the time between counts? a. E(X) = 0.333, SDX) = 0.111 b. E(X) = 0.333, SD(X) = 0.333 Oc. NONE Od. E(X) = 3, SD(X) = 3
- 9. Consider a bank office where customers arrive according to a Poisson process with an average arrival rate of customers per minute. The bank has only one teller servicing the arriving customers. The service time is exponentially distributed and the mean service rate is μ customers per minute. It turns out that the customers are impatient and are only willing to wait in line for an exponential distributed time with a mean of 1/μ minutes. Assume that there is no limitation on the number of customers that can be in the bank at the same time. a. Construct a rate diagram for the process and determine what type of queuing system this correspond to on the form A1/A2/A3. b. Determine the expected number of customers in the system when λ = 1 and μ = 2. c. Determine the average number of customers per time unit that leave the bank without being served by the teller when λ = 1 and µ = 2.The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 15.1 26.3 31.2 38.3 51.3 20.5 22.7 y 2.68 2.38 1.48 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Round r to three decimal places.) Σχ = Ey = Ex? = Ey? = Σχy r = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t = critical t = Conclusion O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Reject the null hypothesis. There is insufficient evidence that p < 0. O…
- What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 16.1 23.3 29.2 38.3 51.3 20.5 22.7 2.68 2.18 1.88 1.03 0.75 2.38 2.20 (c) Find S, a, and b. (Round your answers to five decimal places.) e' Se a = b = (d) Find the predicted optimal time in hours for a dive depth of x = 38 meters. (Round your answer to two decimal places.) hr (e) Find an 80% confidence interval for y when x = 38 meters. (Round your answers to two decimal places.) lower limit hr upper limit hr (f) Use a 1% level of significance to test the claim that ß < 0. (Round your answers to two decimal places.) t = critical t = (g) Find a 90%…e 14-25. A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1-5. Calculate the proportion of days on which (i) Neither car is used (ii) Some demand is refused.If two Normal universes A and B have the some total frequency but the standard deviation of universe A is K time that of the universe B, show that maximum frequency of universe A is (1/k) time that of universe B.
- What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. x 16.1 26.3 29.2 38.3 51.3 20.5 22.7 y 2.68 1.98 1.48 1.03 0.75 2.38 2.20 (b) Use a 1% level of significance to test the claim that ? < 0. (Round your answers to two decimal places.) t = critical t =Average temperature in Winter and Summer in a region for 2016-2019 is given below. Year Winter Summer 2016 20 45 2017 35 44 2018 28 43 2019 29 48 Assume the additive time series model with no trend and using the above data, answer the following questions. 1. Compute two period moving averages MA(2). 2. What is the advantage of computing MA(2). 3. Do you need to compute CMA. Why or why not. 4. Estimate the seasonal factors for Winter and summer. 5. Forecast the average temperature for Fall and Spring 2020 assuming CL=2 and IR=0