It is known to show an exponential distribution where the average lifespan of a type of CPU is eight years. What is the probability that the company that leases the server for five years will encounter a central processing unit failure within the period of use?

It is known to show an exponential distribution where the average lifespan of a type of CPU is eight years. What is the probability that the company that leases the server for five years will encounter a central processing unit failure within the period of use?

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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You were asked to help with an analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers’ AGE at birth (continuous variable in years), mothers’ current HOUSING status (“own” and “not-own”; “own” is the reference group), and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”; “Manhattan” is the reference group). Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status and BOROUGH. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE…
Total DVD and Blu-ray disc sales in 2009 were $8.72 billion. For the purposes of this problem, you will combine DVD and Blue-ray disk sales into one category of DVD sales. A study by In-Stat predicted that "physical disc sales will decline by $4.7 billion by 2014," and that "streaming, on the other hand, should grow from its current $2.2 billion to $6.3 billion over the same time period (2009–2014). d. Write an equation that represents the linear model for streaming videos. Let S = the total sales of streaming videos in billions of dollars, and t = the number of years after 2009. e. In what year do the models predict streaming video sales to exceed DVD sales?
Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poissondistribution. For simplicity, assume that there is only one lane and one worker who can serve atan average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three ormore vehicles ahead of you?
You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “State Island”). Write down the population model that assumes the effect of mother’s AGE at birth on infant weight BW is DIFFERENT for different levels of maternal smoking status (MSS) when adjusted for BOROUGH variable. Specify the name of each predictor in the model and/or what it means. Make sure that it is clear what each predictor means.
Consider the following queuing systems:System 1 An average of 40 customers arrive each hour; interarrival times are exponential. Customers must com-plete two types of service before leaving the system. The first server takes an average of 30 seconds (exponentiallydistributed) to perform type 1 service. After waiting in line, each customer obtains type 2 service (exponentially distrib-uted with a mean of 1 minute) from a single server. After completing type 2 service, a customer leaves the system.System 2 The arrival process for system 2 is identical to the interarrival process for system 1. In system 2, a cus-tomer must complete only one type of service. Service time averages 1.5 minutes and is exponentially distributed. Twoservers are available.In which system does a typical customer spend less time?
cipate worth S Exercise 2.9.8. [S][Section 2.1][Goal 2.1][Goal 2.5] Counting red blood cells. On page 240 of the April 2011 issue of the Bulletin of the American Mathematical Society Misha Gromov wrote that Erythrocytes are continuously produced in the red bone marrow of large bones... at the rate ~ 2.5 million/second or~ 200 billion/day. Adult humans have 20-30 trillion erythrocytes,~ 5 million/ cubic millimeter of blood. [R54] (a) What is an erythrocyte? (b) Check that 2.5 million/second is about 200 billion/day. (c) Use the numbers in the second sentence to estimate the volume of blood in an adult human, in liters. (d) Check your answer to the previous question with a web search.
Ankylosing spondylitis is an inflammatory disease which affects the spine and sacroiliac joint and can lead to the fusing of vertebrae in the spine. Exercise is important in helping manage pain, therefore a pharmaceutical company wanted to test if their new biologic would increase the time a patient could exercise before experiencing discomfort. The following table gives the time (in minutes) seven patients were able to exercise before reporting pain, both at baseline and then again after six months of taking the biologic.Exercise Time (in minutes)Subject 1 Baseline 30 Post-treatment 40Subject 245 40Subject 350 60Subject 435 37Subject 555 60Subject 620 25Subject 775 75Assume the population(s) of all exercise times is (are) normally distributed. Use JMP to test whether the evidence suggests that the time a person with ankylosing spondylitis can exercise before experiencing discomfort increases after taking this new biologic. Validate the test statistic from JMP by computing it manually.…
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?
For the Philippines Basketball Association (PBA) 2013-2014 season, San Mig James Yap was the scoring leader with an average of 33 points per game. The following data shows the average of points per game for the scoring leader from the 2008-2009 season to the 2013-2014 season. Season Average 2008-2009 25 2009-2010 35 2010-2011 29 2011-2012 34 2012-2013 35 2013-2014 33 Use exponential smoothing to forecast this time series. Consider smoothing constant of ɑ = 0.20 and ɑ = 0.30. What value of the smoothing constant provides the best forecast/ What is the forecast of the leading scoring average for the 2014-2015 season? Graph the forecast at ɑ = 0.30.
Assume a single server queueing system with exponential inter-arrival times, and service times. Assume that the expected inter-arrival time is 10 minutes, and the expected service time is 7.5 minutes. We are interested in the expected time the customers spend waiting in queue (in minutes). Develop a Monte Carlo simulation model to estimate Wg Calculate W (expected wait time in queue), and compare it with the previous result
The average lifetime of a certain new cell phone is 5 years. The manufacturer will replace any cell phone failing within 3 years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.What is the median lifetime of these phones (in years)? (Round your answer to four decimal places.)