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

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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…

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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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 51E

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Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.
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We expect poorer countries (X=1) to grow faster (Y=1) than richer countries-the table below displays countries' relative incomes and growth rates. Poorer than average (X=1) Richer than average (X=0) Ten-year growth above Ten-year growth below average (Y=1) average (Y=0) 0.38 0.14 0.13 a) Find the covariance between the two variables. 0.35 b) Interpret in plain words the independence between X and Y. (up to 40 words)
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 60 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 15°C.
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 60 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ? ≈ 13°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit °C upper limit °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will…
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 13°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit °C upper limit °C
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 55 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ? ≈ 22°C.
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ? ≈ 16°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit °C upper limit °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will…
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 14°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit     °C upper limit     °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will…
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 57 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 16°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit     °C upper limit     °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will…
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 60 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ? ≈ 22°C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.) lower limit     °C upper limit     °C (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon…