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17/10/15: Let’s talk about the Law of Small Numbers
trueeconomics.blogspot.com / by Constantin Gurdgiev / Saturday, October 17, 2015
Wonkishly awesome, folks…
Let’s start with a set up
You decide to will flip a coin 4 times in a row and record the outcome of each flip. After you done flipping, you look at every flip that “immediately followed an outcome of heads, and compute the relative frequency of heads on those flips”.
“Because the coin is fair, [you] of course expect this empirical probability of heads to be equal to the true probability of flipping a heads: 0.5.”
You will be wrong. If you “were to sample one million fair coins and flip each coin 4 times, observing the conditional relative frequency for each coin, on average the relative frequency would be approximately 0.4.”
Two researchers, Joshua Miller and Adam Sanjurjo “demonstrate that in a finite sequence generated by i.i.d. [independent, identically distributed] Bernoulli trials with probability of success p, the relative frequency of success on those trials that immediately follow a streak of one, or more, consecutive successes is expected to be strictly less than p, i.e. the empirical probability of success on such trials is a biased estimator of the true conditional probability of success.”
The post 17/10/15: Let’s talk about the Law of Small Numbers appeared first on Silver For The People.
Source: http://silveristhenew.com/2015/10/17/171015-lets-talk-about-the-law-of-small-numbers/
