34. Two individuals, A and B, both require kidney transplants. If she does not re-ceive a new kidney, then A will die after an exponential time with rate uA, andB after an exponential time with rate u B. New kidneys arrive in accordancewith a Poisson process having rate . It has been decided that the first kidneywill go to A (or to B if B is alive and A is not at that time) and the next one toB (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?Act

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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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 with rate uB. New kidneys arrive in accordance with a Poisson process having rate A. It has been decided that the first kidney will go to A (or to B if B is alive and A is not at that time) and the 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?
1. Zombies have appeared in Chicago and every day, each zombie produces 3 new zombies. Suppose that initially there is only one zombie, how many zombies will there be in 7 days? 2. In a rabbit population, each pair produces 2.2 offspring every year (i.e. 1.1 per capita) and the adults have a 0.9 annual death rate after reproduction (and assume the whole population is paired up into mating pairs.) If initially there are 55 rabbits, predict how many there will be in 5 years (rounded to the nearest integer). 3. Consider the same rabbit population, but now a python that lives nearby eats exactly 1 rabbit a month. If initially there are 55 rabbits, how many do you predict will be in 10 years?
Q5. Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages; Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages; and Pat, who stamps 5% of the packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John?
4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate A; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.
3. Suppose that the populations of two species interact according to the relationships below. Let S be snakes and R rabbits. 1 Rk+1 = =Rk+ - Sk 2 Sk+1= -Rk + 2SK == What would the populations of both snakes and rabbits be after 10 iterations?
A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99
n 14 of 16 > Brian and Jennifer are planning to get married at the end of Brian's blood type Jennifer's blood type the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type. 0.25- -0.28 -0.34 AB B 0.13. Suppose a recent study shows that 25% of adults have blood type A, 28% of adults have blood type B, 34% of adults have blood type AB, and 13% of adults have blood type 0. The tree 0.25 0,25 -0.28 B -0.34. AB diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities. 0,28 0.13 What is the probability that Brian and Jennifer share the same 0.25 A 0.34 blood type? Give your answer as a decimal, precise to at least two decimal places. -0.28 B -0.34 AB AB- 0.13. 0.13 0.25 0.28 -B P (Brian and Jennifer have the same blood type) = -0.34. AB 0.13.
4. ) Suppose a virus spreads so that the number N of people infected grows exponen- tially with time t. The table below shows how many days it takes from the initial outbreak to have various numbers of cases. t=# of days N =# of cases 63 8 million 36 1 million How many days since the initial outbreak until the virus infects 40 million people? (Round to the nearest whole number of days)
6. The weather in San José is either sunny or rainy. Suppose that, after a sunny day, there is a 30% chance of having a rainy day, and after a rainy day, there is a 50% chance of having a sunny day. (a) Construct a difference equation model to predict the weather, where Sn is the chance of the nth day being sunny, and Rn is the chance of the nh day being sunny. (b) Suppose today is sunny. What is the probability that the day after tomorrow is sunny? (c) Compute the fixed point for the system. (d) Interpret the fixed point in terms of the long-term behavior of the system.
I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy. E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density function given by. f(t)=(at^2 0=t=50, b(100-t) 50=t=100, 0 elsewhere) i) Show that a = 3/312500 and b= 3/6250 ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km. iii)Sketch the graph of T on the axes below, clearly labelling the scale. iv) Find the expected value and variance of brand E car tyres. v) Find the probability that the lifetime of brand E car tyres lies within two standard…
7. The new 'Tigercat' sports car has an idle loping problem as about 10 per cent of the Tigercats have an unstable fluctuating engine speed when they are idling. An engineering 'fix' is put in a production pilot lot of a hundred cars. (a) If the fix has no effect on the problem, how many cars would you expect to have the fault? (b) If only two of the pilot lot have the idling fault, and the other ninety-eight cars are not defective, would you conclude that the fix has a significant effect? (Hint: Show that the probability of getting two or less defectives in a sample size of a hundred, given that the fix has no effect, is very small indeed.)
1. Two species are said to be symbiotes if they help each other to survive. For instance, elown fish and sea anemones are symbiotes (they protect each other from different types of predators). Say in some region, without sea anemones to shelter them, the clown fish population is stable (that is, the clown fish population in the k + 1-th season is the same as the population in the k-th season). However, for each sea anemone present, an extra 0.2 clown fish are present in the next season. Similarly, in the absence of clown fish, the sea anemone population in the k + 1-th season is only 70% of the population in the k-th season. However, for each clown fish present, an extra 0.2 anemones are present the next season. (a) Write down difference equations for the number of clown fish and sea anemones in the k + 1-th season in terms of the clown fish c& and sea anemones ar in the k-th season. (b) Write the system of difference equations above as a matrix equation, then diago- nalize the matrix.

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