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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(b) Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: [Pusat Servis Cuci Kereta Ali Baba dibuka 6 hari seminggu, tetapi hari yang paling sibuk selalunya pada hari Ahad. Daripada data yang lepas, Kedai Cuci Kereta Ali Baba menganggarkan bahawa kereta kotor tiba pada kadar satu setiap dua minit. Satu kereta pada satu masa dibersihkan dalam contoh saluran menunggu satu saluran ini. Dengan andaian ketibaan tahuran Poisson dan masa perkhidmatan eksponensial, carikan yang berikut:] i) Compute the average number of cars in line. [Kirakan purata untuk bilangan kereta yang menunggu dalam baris.) ii) Calculate the value of probability that there are no car in the system. [Kirakan nilai…
9 Question 4 A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 16% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package. The engineer weighs 129 bags and finds that 27 of them are over-filled. He plans to test the hypotheses Ho: p = 0.16 versus H:p> 0.16. What is the test statistic? Z = (Please round your answer to two decimal places if necessary.)
Exercise 17. A manufacturer examines its records over the last year on a component part received from outside suppliers. The breakdown on source (supplier A, supplier B) and quality (H: high, U: usable, D: defective) is shown in the two-way contingency table.H U DA 0.6937 0.0049 0.0014B 0.2982 0.0009 0.0009The record of a part is selected at random. Find the probability of each of thefollowing events.a. The part was defective.b. The part was either of high quality or was at least usable, in two ways: (i) by adding numbers in the table, and (ii) using the answer to (a) and theProbability Rule for Complements.c. The part was defective and came from supplier B.d. The part was defective or came from supplier B, in two ways: by finding the cells in the table that correspond to this event and adding their probabilities, and (ii) using the Additive Rule of Probability.
A grasshopper hops between three flowers, labelled 1, 2, 3. It starts from flower 1. Once it arrives at a flower, it sits there for a period of time distributed exponentially with parameter 2. Then it makes a jump, as follows: if it is located on flower 1, it jumps to 2 or 3 with equal probability; if it is located at 2, it jumps to 3, and if it is at 3, it jumps to 2. (a) Model the grasshopper using a continuous-time Markov chain. Find the states, the initial distribution and the jump rates! (b) What is the probability that at time t the grasshopper will sit on the third flower?
This is a multipart question 6.) Diesel Dave has modified his massive truck to combat global cooling, and to roll coal on his neighbor Environmentalist Ed. With each blast of diesel exhaust fumes, Diesel Dave releases sulfur dioxide in a giantblack cloud. Every morning as Diesel Dave is leaving home he rolls coal into Environmentalist Ed's yard. Not surprisingly, Environmentalist Ed is diligently collecting data on the air quality in his yard. Suppose Diesel Davereleases sulfur dioxide in a normally distributed manner with a mean of 2800 ppm and a standard deviation of 120 ppm. What is the probability that on a random morning he will release sulfur dioxide greater than 3000ppm? Suppose in order to sue Diesel Dave, Environmentalist Ed needs the daily average level of sulfur dioxide emissions to exceed 3000 ppm. However, he can choose to take his mean measurement over 2, 3, or 15 days. Which number of days would maximize Environmentalist Edís chances of suing Diesel Dave? (Hint: What…
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…
In the B&K model of Example 18.5-1, suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Suppose further that will add a fourth counter. Counters 1,2, and 3 will open based on increments of two customers and counter 4 will open when there are 7 or more in the store. (a) The steady-state probabilities, for all . (b) The probability that a fourth counter will be needed. (c) The average number of idle counters.
Given two independent Poisson processes of rates λ1 and λ2, what is the probability that process 1 has more arrivals than process 2 in 1 second?
Question 87 parts A and B
a. A researcher studied the effect of social influence on drinking behaviour. Sixty people were randomly assigned to one of three conditions where they were given a soft drink to consume while waiting for the experiment to supposedly begin. An experimental assistant, posing as another participant, was also given a drink. In one condition, the assistant sipped the drink at a faster rate than the research participant; in another condition, the assistant sipped the drink at the same rate as the participant; and in the last condition, the assistant sipped the drink at a slower rate than the participant. The time it took each participant to consume his or her drink was measured.
On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 15 trials of this experiment: 212, 236, 217, 235, 164, 257, 175, 285, 202, 193, 231,152, 269, 296, 186 Send data to calculator Find 30th and 75th percentiles for these reaction times.
Consider two assets with returns: rị = 3 (:) r2 = in two states. If the 1 has a return (:) portfolio z = find the value of a.

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