Please answer only the Question C. Thank you Question 4Consider a birth death model with birth rates A, in states n = 0, 1, ...and death rates 4, in states n = 1, 2, ..(a) Give the detailed balance conditions for the equilibrium probability of being instate n, forn= 0, 1, ... and explain how they are derived.(b) Using the detailed balance conditions derive an expression p, and state anycondition needed to ensure that the equilibrium distribution exists.(c) i Now consider the M/M/1 queue with arrival rate i and service rate u andexplain how it canbe modelled as a birth death model.ii. For the M/M/1 queue derive the form of p„ , the equilibrium distribution ofthe number ofcustomers present, and give any conditions needed to ensure the existenceof theequilibrium distribution. Derive the mean value of the equilibriumdistribution

Name: Please answer only the Question C. Thank you Question 4Consider a birt
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please answer only the Question C. Thank you Question 4Consider a birth death model with birth rates A, in states n = 0, 1, ...and death rates 4, in states n = 1, 2, ..(a) Give the detailed balance conditions for the equilibrium probability of being

Consider a birth death model with birth rates, lambda in states n = 0, 1,... and death rates mu in…

Math

Statistics

Question 4 Consider a birth death model with birth rates A, in states n = 0, 1, ... and death rates 4, in states n = 1, 2, .. (a) Give the detailed balance conditions for the equilibrium probability of being in state n, for n= 0, 1,... and explain how they are derived.

Question 4 Consider a birth death model with birth rates A, in states n = 0, 1, ... and death rates 4, in states n = 1, 2, .. (a) Give the detailed balance conditions for the equilibrium probability of being in state n, for n= 0, 1,... and explain how they are derived.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 5E: Population Genetics In the study of population genetics, an important measure of inbreeding is the...

See similar textbooks

Similar questions

Altmans z-score Altmans z-score is a financial tool for predicting insolvency in a business. For a certain company, the z-score formula is z=0.84+0.6StockpriceOutstandingsharesTotalliabilty In this exercise, we assume that thre are 45, 000 outstanding shares at a price of 4.80 each. a. Use L, for total liability, in dollard, and give a formula for the z-score for this company. b. Would a larger total liability idicate a better or worese outlook for the company? c. A z-score of 1.81 or lower indicates a high probability of insolvency. What is the smallest value of L that will give a z-score that indicates a high probability on insolvency?
Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?
Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .
Question 3 Hermie's average 5-day natural gas usage rate is 5.9Therms5days . What are her 1-day, and 8-day, natural gas usage rates? 1.18Therms1day,7.375Therms8days 0.7375Therms1day,9.44Therms8days 1.18Therms1day,9.44Therms8days 0.7375Therms1day,7.375Therms8days
1(a) A researcher hypothesized that joining a fitness training program could result in change of weight. To test this hypothesis empirically, 15 participants were invited to complete the fitness training program. The changes of weight (in kg) of the 15 participants were found to be -1.0, -1.1, -1.2, -0.9, -0.8, -0.1, -0.4, -0.6, -0.9, -0.3, -0.5, -0.9, -1.5, -1.1, and -1.3 respectively. (i) State the non-directional null and alternative hypothesis of this study. Using .05 as the level of significance, conduct an appropriate statistical test on the results and state (ii) the steps to compute the test statistics; and(iii) the conclusion of your statistical test and your reasoning to arrive at your conclusion. (b)If the mean height of a population of university students is 166cm (μ=166) and the standard deviation is 8cm (? = 8): (i) What is the probability of drawing a random sample of university students whose mean height is larger than 168cm if sample size is equal to 1. 30? 2. 100?
Question: Solve the following problem using M/M/1 queueing model analytically: Consider a service facility with a single server and assume M/M/1 queueing model, for ? values of [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] and ? value of 4. Find the below steady state parameters: ??: Steady-state probability of having ? customers in system, assume ? = [0,1,2,3,4,5,6,7,8,9]. ?: Long-run time-average number of customers in system. ??: Long-run time-average number of customers in queue. ?: Long-run average time spent in system per customer. ??: Long-run average time spent in queue per customer.
Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.
The price of a stock is modeled with a geometric Brownian motion with drift μ=-0.25 and volatility σ=0.4. The stock currently sells for $35. What is the probability that the price will be at least $40 in 1 year?
2.2 The demand for a product varies from month to month. Based on data from past years, the following probability density function shows the probabilities of MNM company’s monthly demand. Probabilities of MNM company's monthly demand Unit Demand P(X=x) 1200 0.19 2100 0.30 3300 0.40 3800 0.11 c) Calculate the standard deviation. d) Each unit produced costs the company $8.00, and each unit is sold for $25.00. How much will the company gain or lose in a month if they stock the expected number of units demanded but sell 2100 units?
Question A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses? Select the correct answer below: H0: p=0.18; Ha: p<0.18 H0: μ=0.18; Ha: μ<0.18 H0: p=0.18; Ha: p>0.18 H0: p<0.18; Ha: p=0.18
[Question 19 The common stock of DEE Bhd. has a beta of 1.24 and an actual expected return of 13.25 percent. The risk-free rate of return is 3.7 percent and the market rate of return is 11.78 percent. Which one of the following statements is TRUE given this information? Select one: A. The stock has less systematic risk than the overall market. B. The actual expected stock return will graph above the security market line. C. The stock is currently underpriced. D. The actual expected stock return indicates the stock is currently overpriced.
Question 17 Suppose Carole has a total wealth of $100,000 and a utility described by U = E -A She has a risk aversion coefficient of A-1. She can borrow and lend/invest at the risk-free rate of 2.8%. Suppose the optimal risky portfolio has an expected return of 12% and a standard deviation of 27.5%, What is her optimal amount to borrow or lend/invest at the risk free rate? Indicate investing/lending as a positive number and borrowing as a negative number. Round to the nearest cent ($0.01). Your answer should not include the $ sign. If your answer is $25.34, it should be written as 25.34. Question 18 Ayear ago, an investor bought 200 shares of a "no-load" mutual fund at $10.01 per share. No-load funds do not change "entry fees or "exit" fees when buying or redeeming shares. Sometime during the year, the fund paid dividends of $0.71 per share and the fund paid capital gains of $0.14 per share - and these payments were reinvested in the fund at an average price of $10.73 per share…