(24) Consider an experiment where we collect N = 106 molecules of a gas in closed...

 

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!

Answer rating: 100% (QA)

EXN 2 VxN 4 PIXN 0005 N P P1XN ... View the full answer