Boramey Chhay All the Calc 3 you need for Help Lab
Tue, Aug. 30 12:10pm (MATH …
Janos Englander (CU Boulder) Turning a coin instead of tossing it
So it's been a while since Calculus 3 and now you need to be able to answer student questions about it in the Help Lab. Not a problem! This talk will be a review of stuff from Calculus 3 that you may or may not have forgotten.
Given a sequence of numbers in , consider the following experiment. First, we flip a fair coin and then, at step , we turn the coin over to the other side with probability , . What can we say about the distribution of the empirical frequency of heads as ?
We show that a number of phase transitions take place as the turning gets slower (i.e. is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is . Among the scaling limits, we obtain some well known special (Uniform, Gaussian, Semicircle and Arcsine) laws.
The talk is intended to a general audience and no expertise in probability is assumed!