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- A five years Business Informatics student studying at TU Wien does some temporary substitute work on the banking sector every 31 days on average, and this time follows an exponential distribution. After acquiring one of these works, its duration is also aleatoric, exponentially distributed and its mean duration is 60 daysThe money earned depends on the total number of days worked in each contract, paid at $100 daily. For unemployment periods, the student has taken out an insurance for which $50 is paid for each day on the dole. Build a queuing model to establish the mean annual income (1 year = 365 days) that the student earns. (Hint: single server, finite customer population of 1.)The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 33 32 33 32 39 43 56 48 44 49 44 56 58 60 60 63 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two…The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2012 2010 2012 2014 2016 336.5 363.5 398.1 Year CO, Emissions 2018 424.8 451.1 Year 2022 2024 2026 2028 2030 Co, Emissions 559.2 591.9 628.7 665.1 707.1 2020 2032 743.7 Using x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions, write the equation of the linear function that models these data. (Round all numerical values to two decimal places.) Hint: Let x 0 in 2010. y(x) =
- Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with A = 0.0003. • What proportion of the fans will last at most 10,000 hours? • What proportion of the fans will last at least 7000 hours? a. 0.0498, 0.8775 Ob. NONE Oc 0.0498, 0.1225 Od.0.0502, 0.1225The monthly percentages of all shipments received on time are Monthy Proportion of On Time Shipments 72 81 78 90 83 85 90 82 89 81 85 84 78 88 Using the better method (4 month moving average or exponential smoothing with α=0.3), what is the forecast for next month? (round up to the nearest integer if your answer is not an integer)The Baytown Post Office has 4 stations for service. Customers line up in single file for service on an FIFO basis. The mean arrival rate is 32 per hour, Poison distributed, and the mean service time per server is 6 minutes, exponentially distributed. Compute the operating characteristics for this operation. Does the operation appear to be satisfactory in terms of: (a) Postal workers' (servers') idle time; (Round answer to 3 decimal places, e.g. 2.750.) (b) customer waiting time and the number waiting for service; (c) the percentage of the time a customer can walk in and get served without waiting at all?
- A researcher is interested in finding out how the past average daily values of the stock prices of a firm A determine the current average daily value of its stock price. Let pt ( measured in dollars) denote the average daily value of the stock price of firm A at time t. The researcher collects data on the average daily values of the stock prices of the last quarter of 2017, i.e., t = 1,2, dots,90 and estimates the following autoregressive model with 1 lag of pt: hat(p)t = 2.48 +.05pt.1bar (R)² = 0.512, SER = 13.14. (1.13) (0.64) The standard errors are given in parentheses. Suppose that the actual average daily value of the stock price on January 2, 2018 was $506.12 and the average daily value of the stock price on December 31, 2017 was $445.12. The forecast error in the estimation of the average daily value of the stock price on January 2, 2018 will be $ (Round your answer to two decimal places.) This is all the info in the questionA statistical program is recommended. Electric power consumption is measured in kilowatt-hours (kWh). The local utility company offers an interrupt program whereby commercial customers that participate receive favorable rates but must agree to cut back consumption if the utility requests them to do so. A certain company cuts back consumption at 12:00 noon Thursday. To assess the savings, the utility must estimate the company's usage without the interrupt. The period of interrupted service was from noon to 8:00 p.m. Data on electric power consumption for the previous 72 hours are available. Time Period 12-4 a.m. 4-8 a.m. (b) Compute 8-12 noon 12-4 p.m. 4-8 p.m. 8-12 midnight 41,310 Time Period 12-4 a.m. 4-8 a.m. 8-12 noon Monday 12-4 p.m. 4-8 p.m. 8-12 midnight 124,299 123,666 113,555 111,717 Seasonal Index 0.3262 0.4484 1.3647 Tuesday 1.6992 (a) Is there a seasonal effect over the 24-hour period? O No, the time series plot indicates a linear trend with no seasonal effect. O Yes, the…In an M/MA queueing system, the arrival rate is 5 customers per hour and the service rate is 9 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) 2.