42. Consider the following modification of a branching process: A matureindividual produces children according to the generating function g(t).However, an individual becomes mature with probability a and dies beforematurity with probability 1-a. Throughout X(0) = 1, that is, we startwith one immature individual.(a) Find the generating function of the number of individuals in the firsttwo generations.(b) Suppose that the offspring distribution is geometric with parameter p.Determine the extinetion probability

The ratio of the number of outcomes favourable for the event to the total number of possible…

Answered: 42. Consider the following modification…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

16. The resident population P of the District of Columbia (in thousands) from 1995 through 2005 can be modeled by where t is the year, with t = 0 corresponding to 2000. (Source: U.S. Census Bureau) (a) During which year, from 1999 through 2005, was the population the greatest! P = 0.26943 – 2.048/² – 0.73t + 571.9, -1
3. Jobs arrive in a computer queue in the manner of a Poisson process with intensity λ. The central processor handles them one by one in the order of their arrival, and each has an exponentially distributed runtime with parameter , the runtimes of different jobs being independent of each other and of the arrival process. Let X (t) be the number of jobs in the system (either running or waiting) at time t, where X (0) = 0. Explain why X is a Markov chain, and write down its generator. Show that a stationary distribution exists if and only if λ < μ, and find it in this case.
According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.
A9. If the total benefit function is B = 192M – 4M^2, the total damage function is D = A2, ⍺ = 0.5 and there is no discounting where: M is the level of emissions. A is the stock of the pollutant. ⍺ is the linear decay rate of A a) What are the steady-state levels of M and A? b) Assuming now that we have some discounting and r = 0.2, where r is the social consumption discount rate. What are the new steady state levels of M and A?
2. A random variable X has a p.d.f. f(x) given by √(1-x)6 0
Let i, denote the effective annual return achieved on an equity fund achieved between time (t-1) and time t. Annual log-returns on the fund, denoted by In(1+i), are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and σ = 14%. An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%.
8 The failure of a circuit board interrupts work that utilizes a computing system, until a new board is delivered. The delivery time, Y, is uniformly distributed on the interval one to six days. The cost of a board failure and interruption includes the fixed cost co of a new board and a cost that increases proportionally to y². If C is the cost incurred, C = Co + c₂y². (a) Find the probability that the delivery time exceeds three days. (b) In terms of co and c₁, find the expected cost associated with a single failed circuit board.
Let X represent the lifetime of a component, in weeks. Let Y represent the lifetime of the component in days, so Y = 7X. Suppose X ~ Exp(1). Let Fy be the cumulative distribution function of Y and let Fy be the cumulative distribution function of X. Show that Fy(y) = 1 e¯e-Ày/7. [Hint: F,(y) = P(Y < y) = P(7X

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS