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- Consider the following time series data. Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. Mean absolute percentage error. If required, round your intermediate calculations and final answer to two decimal places._____________%In the article “The World's Longest Continued Series of Sea Level Observations” (M. Ekman, Paleogeography, 1988:73–77), the mean annual level of land uplift in Stockholm, Sweden, was estimated to be 4.93 ± 0.23 mm for the years 1774–1884 and to be 3.92 ± 0.19 mm for the years 1885–1984. Estimate the difference in the mean annual uplift between these two time periods, and find the uncertainty in the estimate.To seethe effect of a relatively small error in the estimate of the amountof carbon-14 in a sample being dated, consider this hypotheticalsituation: A bone fragment found in central Illinois in the year 2000 contains 17% of its original carbon-14 content. Estimate the year the animal died.
- The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).a) Find the probability that the demand will exceed 200 cfs during the early afternoon on arandomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will exceed capacity on a randomly selected day isonly .01?Is there a relationship between smoking and alcohol consumption? No Alcohol Low Alcohol Medium Alcohol High Alcohol Marginal Total Never Smokes 450 205 190 75 Smoker 425 255 170 30 Marginal Total Round each of the following to two decimal places: What is the expected frequency of people who never smoke and do not consume alcohol? What is the expected frequency of smokers who do not consume alcohol? What is the expected frequency of people who never smoke and consume high amounts of alcohol? What is the expected frequency of smokers who consume high amounts of alcohol?Consider a grocery store between the hours of 6 and 8pm on a weeknight. Suppose two checkout lanes are typically open, each checkout can handle customers with any number of items, and each checkout has a dedicated employee. It has been observed that checking out takes a mean of 1.5 minutes per customer and that this is approximately normally distributed with a standard deviation of .3 minutes. The mean amount of time between customer arrivals at the checkouts is 1 minute and can be approximated by an exponential distribution. A: Model the scenario where a single queue is used to feed both checkout lanes (similar to the bank example with two tellers). What is the average flow time of a customer? B: Model the scenario where each checkout lane has its own separate queue, and assume that half of the customers go to queue 1 and the rest go to queue 2. What is the average flow time of a customer in this setup? Hint: Split the customer arrivals in half (i.e., double ??) and model just a…
- Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data (in years of life): (78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79) Does this sample indicate that life expectancy has increased? Test an appropriate hypothesis and state your conclusion (use a 5% level of significance). Be sure to check the necessary assumptions and conditions before conducting your test. Construct A 90% confidence interval for the true average age of death for the…The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?By first calculating, and then combining, the number of counts in each individual 30- second period, what does student A determine as the average decay rate (in counts/sec), and what is its uncertainty?
- Consider the following time series data: Using the naïve method (most recent value) as the forecast for the next week, compute thefollowing measures of forecast accuracy:a. Mean absolute errorb. Mean squared errorc. Mean absolute percentage errord. What is the forecast for week 7?The operator of a pumping station has observed that demand for waterduring early afternoon hours has an approximately exponential distribution with mean 1000cfs (cubic feet per second).a) Find the probability that the demand will exceed 700 cfs during the early afternoonon a randomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will be below the capacity on a randomly selectedday is 0.995?c) Of the three randomly selected afternoons, what is the probability that on at least twoafternoons the demand will exceed 700 cfs? 2. Let Y1 and Y2 be random variables with joint density functionf(y1, y2) = (6/7(y^2+y1y2/2) 0 < y1 < 1, 0 < y2 < 2,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Find P(0 < Y1 < 0.3, −2 < Y2 < 1).c) Find P(0.6 < Y1 < 1|0 < Y2 < 1). 3.The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2), 0 <…Suppose the daily demand for petrol at a certain petrol station is nomally distributed with a mean of 6849 litres and a standard deviation of 342 litres. This morning the manager notices that there is 7105.5 litres in storage with the next delivery coming only at closing. a) What is the probability that there will be enough petrol to meet the daily demand? (Rounded to 4 decimal places)Answer b) If a year has 365 days, how many days do you expect the demand to be less than 7105.5 litres? (Rounded to the nearest integer)