(24) Consider an experiment where we collect N = 106 molecules of a gas in closed...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(24) Consider an experiment where we collect N = 106 molecules of a gas in closed container. The probability a gas molecule is on the left or right side of the container is modeled by a Bernoulli random variable. Thus for N Bernoulli trials the expectation of the number of molecules on the right is N/2 with variance N/4. Use the problem (22), and the CLT, to find a bound for the probability that the number of molecules on the right fluctuate by more than 0.5%. In other words, find a bound for P(|XN/2) > 0.005N). This demonstrates, with no further assumptions, that there is a finite and calculable probability that all the air in a room would rush to one side only. Let's just hope we're on the right side! (24) Consider an experiment where we collect N = 106 molecules of a gas in closed container. The probability a gas molecule is on the left or right side of the container is modeled by a Bernoulli random variable. Thus for N Bernoulli trials the expectation of the number of molecules on the right is N/2 with variance N/4. Use the problem (22), and the CLT, to find a bound for the probability that the number of molecules on the right fluctuate by more than 0.5%. In other words, find a bound for P(|XN/2) > 0.005N). This demonstrates, with no further assumptions, that there is a finite and calculable probability that all the air in a room would rush to one side only. Let's just hope we're on the right side!
Expert Answer:
Related Book For
Fundamentals of Cost Accounting
ISBN: 978-0077398194
3rd Edition
Authors: William Lanen, Shannon Anderson, Michael Maher
Posted Date:
Students also viewed these business communication questions
-
As the company Treasurer, the Board of Directors has asked you to comment upon a proposal to initiate dividend payments to the company's common shareholders. The Board wants you to address: What...
-
The board of directors of General Wheels Co. is considering six large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit ( net...
-
The board of directors of Earth Rock's!, a nonprofit organization focused on environmental protection, hypothesizes that individuals are more likely to donate if they see evidence that their...
-
What is food processing ? Different types of food processing methods Briefly explained
-
In an AP-AOL sports poll (Associated Press, December 18, 2005), 272 of 394 randomly selected baseball fans stated that they thought the designated hitter rule should either be expanded to both...
-
a Show correcting journal entries, if appropriate, for the following errors. Subsidiary ledgers are used. i Payment for motor vehicle $26 400 ($24 000 + $2400 GST) was processed to the office repairs...
-
Net present value and net present environmental impact added have a number of similarities and differences. List and explain these. Consider the arguments for and against discounting future...
-
Why do you think Maury Mills got in the shape it is? What are some of the mistakes you think they may have made in managing their human resources? What would you recommend that Dana and Anne do to...
-
Rumor has it that GOJEK is planning to issue its series G of preferred share in September 2020. This series will promise an Rp.1.000,000 per share return annually. You are interested to buy this...
-
From Exercise 10A-3, prepare a schedule of accounts payable and verify that the total of the schedule equals the amount in the controlling account. Exercise 10A-3:
-
Solve the differential equations by part A) and part B). 1+t y' ,1 <1 <2, y(1) = 2 with h = 0.5. 1+y A). With one step of the Taylor-series method of order 2. B). With one step of the Taylor-series...
-
Select a city near their hometown to focus on and explore. Students will produce a three page briefing on the current state of the city including demographics, services, and community assets. Be sure...
-
Pounds of Trouble: Analyzing Exchange Rate Variances Michael A. Harris Graduate Student Brigham Young University Steven D. Smith Associate Professor Brigham Young University Monte R. Swain Professor...
-
Quality Brick Company produces bricks in two processing departments-Molding and Firing. Information relating to the company's operations in March follows: a. Raw materials used in production: Molding...
-
k ces Coram Audio makes wireless headphones. Each pair of headphones comes with a travel case. Since its founding, Coram has manufactured its own travel cases. Recently, Holmur Travel Gear (HTG), a...
-
What is search warrants and overview of laws covering it? What is the chain of custody overview of laws covering it? What is the best practice of seizing electronic evidence? Resources Read the...
-
(30 Pts) Write a class called Student. The class must have two fields: name of the String type and gpa of the double type. Write all the necessary constructors, getters, setters, and toString()...
-
If the joint cost function for two products is C(x, y) = xy2 + 1 dollars (a) Find the marginal cost (function) with respect to x. (b) Find the marginal cost with respect to y.
-
Mission Electronics manufactures and sells basic DVD players for sale under various generic store brand names. The cost of one of their models follows: Materials . . . . . . . . . . . . . . . . . . ....
-
Noonan Division has total assets (net of accumulated depreciation) of $2,200,000 at the beginning of year 1. One of the assets is a machine that has a net book value of $200,000. Expected divisional...
-
A manufacturing company has the following average times (in days): Transporting product. . . . . . . . . 3 Manufacturing product . . . . . . .5 Inspecting product . . . . . . . . . . 2 Storing...
-
What is a heat engine? Calculate its thermal efficiency.
-
What are the differences between a heat pump and a refrigerator?
-
\(7 \mathrm{~mol}\) of an ideal gas \(\left(C_{V}=5 \mathrm{cal} ight)\) was initially at \(30^{\circ} \mathrm{C}\) and \(2 \mathrm{~atm}\). The gas was transferred to the state when the temperature...
Study smarter with the SolutionInn App