2. Two individuals, A and B, both require kidney transplants. If she does not receive a new kidney,then A will die after an exponential time with rate iA, and B after an exponential time withrate uB. New kidneys arrive in accordance with a Poisson process having rate A. It has beendecided that the first kidney will go to A (or to B if B is alive and A is not at that time) andthe next one to B (if still living)(a) What is the probability that A obtains a new kidney?(b) What is the probability that B obtains a new kidney?(c) What is the probability that neither A nor B obtains a new kidney?(d) What is the probability that both A and B obtain new kidneys?

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Answered: 2. Two individuals, A and B, both…

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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1. Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores follow test scoresS group 7 46 86 629 5 5 3 4 4 7 2 2 2 471 2 1 5 5 1) constant sound 2) random sound 3) no sound
Consider a service facility with four clerks. Clerk one works at rate 14/hour; Clerk two at rate 18/hour; Clerk three at rate 20/hour; and Clerk four at rate 16/hour. All service times are independent and exponential. If when you arrive there is already one person waiting, what is your expected waiting time?
A spacecraft navigation system consists of components of two types - A and B - connected in a series-parallel arrangement, as in Figure 1.2. A B A B B Figure 1.2 Illustration of series-parallel system The system will function as long as at least one component of each type functions. The probability that a type A component will function correctly throughout the planned lifetime of the spacecraft is 0-9; the corresponding probability for a component of type B is 0-8. Components may be assumed to fail independently of one another. The numbers of components of the two types may be varied in order to adjust the probability of failure of the navigation system. (a) Show that a requirement that the probability of failure of the entire system should be less than 1% may be met by using three components of each type (as in the diagram above). (b) If components of type A weigh 1 kg, while those of type B weigh 2 kg, what is the composition of the most reliable navigation system weighing 11 kg or…
1
2. Iconic memory is a type of memory that holds visual information for about half a second (0.5 second). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table for this between-subjects designs. G=114 ΣΧ2 = 878 N=18 0 12 11 6 10 8 7 T = 54 M=9 SS=28 Delay Before Recall (in seconds) 0.5 8 4 10 6 3 5 T = 36 M = 6 SS = 34 1.0 4 b. Compute eta-squared to measure the effect size. WOH 4 2 5 7 2 T=24 M=4 SS = 18 a. Do the data indicate that delay to recall had a significant impact on number of words recalled? Use the hypothesis testing steps & alpha = .05. Compute any necessary post-hoc tests.
6.
Freddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172. Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy provided, you ran a t-test for independent samples. These are the results (α = .05). t-Test: Two-Sample Assuming Unequal Variance Current…
43. Six thousand light bulbs light a large hotel and casino marquee. Each bulb fails completely at random, and each has an average lifetime of 3,280 hours. Assuming that the marquee stays lit continuously and bulbs that burn out are replaced immediately, how many replacements must be made each year on the average? 44. The owner of the hotel mentioned in Problem 43 has decided that in order to decrease the number of burned-out bulbs, she will replace all 6,000 bulbs at the start of each year in addition to replacing the bulbs as they burn out. Comment on the effectiveness of this strategy.
The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A andB with expected lifetime 0.25 years and 0.5 years, respectively. When a bulb’s life ends, it stops working. You start with new bulb of type A at the start of the year. When it stopsworking, you replace it with a bulb of type B. When it breaks, you replace with a type Abulb, then a type B bulb, and so on.1. Find the expected total illumination time (in years), given you do exactly 3 bulb re-placements2. Your replacements are now probabilistic. If your current bulb breaks, you replaceit with a bulb of type A with probability p, and with type B with probability (1 –p). Find the expected total illumination time (in years), given you do exactly n bulbreplacements, and start with bulb of type A
1
Digi-Key is a large distributor (but not manufacturer) of electronic components. They receive shipments of components from manufacturers and sell them on to other manufacturers, consumers, and hobbyists. An electrical fuse is generally a small device meant to protect other electrical components from damaging surges of electrical current. Suppose Digi-Key receives shipments of a particular fuse in boxes of 20,000 fuses. The manufacturer of this fuse claims that just 1 out of every 100 fuses is defective. Digi-Key draws 50 fuses randomly from each box and tests them using an error-free method. If it finds 2 or more defective fuses in its sample of 50 fuses, it sends that box back to the manufacturer and gets a replacement box. (Because there are 20,000 fuses in a box--much bigger than 50--you may treat this as if it is sampling with replacement even though it is not really.) Compute the probability that Digi-Key sends a box back to the manufacturer if the manufacturer's claim (that…

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