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--- science:phd-notes:2025-05-13-porter-thomas-fluctuations [2025/05/26 12:38] – jon-dokuwiki
+++ science:phd-notes:2025-05-13-porter-thomas-fluctuations [2025/05/26 12:43] (current) – jon-dokuwiki
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-The law of large numbers tells us that the sample average will converge to the expected value $\mu$ as $n$ goes to infinity. The CLT states that as $n$ gets larger, the distribution of $\bar{X}_n$ gets arbitrarily close to the normal distribution with a mean of 1 and a variance of $2/n$.
+The law of large numbers tells us that the sample average will converge to the expected value $\mu$ as $n$ goes to infinity. The CLT states that as $n$ gets larger, the distribution of $\bar{X}_n$ gets arbitrarily close to the normal distribution with a mean of 1 and a variance of $2/n$ (The PT distribution has a mean of 1 and a variance of 2).
 Let us quickly check that this is true! Let's say that $n = 1000$ and with some quick Python magic: