5. (i) Show that the chance that an exponentially distributed variable takes on a valuebelow its mean is more than 60% and that the chance that the value will be below halfof the mean is almost 40%.(ii) When are exponentially distributed interarrival (service) times reasonable / unrea-sonable for a queuing system?

Given the chance that an exponentially distributed variable takes on a value below its mean is more…

Answered: 5. (i) Show that the chance that an…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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6. An economist studies the relationship betweenthe price (x) and weekly demand (y) of a certainproduct. Assume the SLR model utility test findsevidence of a linear relationship between priceand demand. Find the appropriate intervalestimate for the mean demand for all weekswhen the price is $31. We know: n = 5 , X-bar = 30,sx2 = 10 , MSE = 12.1 , and Y-hat = 181 − 2.7x.
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58. Fit a straight line trend by least squares method and tabulate the trend Pvalues from the following figures of production of a cement factory : Year Production ('000 tonnes) : 2008 77 2009 88 2010 94 2011 2013 2012 91 2014 90 85 98
4. Movements along versus shifts of demand curves Consider the market demand for chicken wings. Complete the following table by indicating whether an event will cause a movement along the demand curve for chicken wings or a shift of the demand curve for chicken wings, holding all else constant. Event An increase in income of consumers An increase in the price of burgers (a substitute for chicken wings) An increase in the price of chicken wings Movement Along Shift O
4 Chemical Oxygen Demand (COD) is a necessary water fine parameter due to the fact similar to BOD, it affords an index to examine the effect discharged wastewater will have on the receiving environment. Table 4 shows the means for the removal reduction of COD in wastewater by three different treatment methods. Test the hypothesis that the reduction percentage is no different for each treatment method. Use the 5% level of significance.
6. A small company can employ 3 workers. Each worker independently stays on the job for an exponentially distributed time with a mean of one year and then quits. When a worker quits, it takes the company an exponentially distributed time with a mean of 1/10 of a year to hire a replacement for that worker (independently of how long it takes to replace other workers). If the company takes in $1000 per day in revenue when it has 3 workers, $800 per day when it has 2 workers, and $500 per day when it has 0 or 1 workers, what is the company's long-run average daily revenue?
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17. A risk manager would like to simulate the price of a stock using the discretized GBM, where St+At = St + µS{At+√Ã£$£€ where μ and o denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.5% and the weekly volatility is 4%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of μ? (a) = 26.4% (b) û = 30.16% (c) û = 4.5% (d) û = 17.94% 18. Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift μ = 0.01 and an annual volatility of o= 0.25. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GBM, the future price at T, i.e. ST, given today's spot price, St, is with TT-t and €~ = (a) 21.51% (b) 35.48% (c) 51.1% (d) 30.47% ST= St x exp (μ x exp [(μ-27 ) XT + √F X 0 Xe] N (0, 1).
Problem : The following system has a radar, a computer and an auxiliary unit connected in series as shown with mean time between failures (MTBF’s) of 91,202 and 500 hours respectively. MTBF=91 HRS MTBF=202 HRS MTBF=500 HRS INPUT RADAR COMPUTER AUXILIARY OUTPUT SYSTEM Determine the following. The unit reliability of each component. System reliability * System MTBF for an operating period of 10 hours
3. Show your complete solution.
3. In the following example, a cohort of six individuals was followed for 100 days after an outbreak of a viral infection in a hospital ward. The graph below shows how many days each subject remained in the study as a non-case (not infected). Those who completed the study as non-cases reached 100 days - the rest fell ill and did become cases. Since we know person-time is used to determine the amount of time at risk, calculate the total time contributed by all six subjects in this study. Note for submission: please make sure to include your units and interpretation in your Worksheet so you have it for review for the midterm, even if Blackboard doesn't allow for this information to be included in your submitted answer! Calculating Person-days F 64 E 100 D. 100 37 55 12 20 40 60 80 100 Days

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