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> You cannot calculate the EV of a random variable X by taking the mean of random samples drawn from the distribution of X My understanding of statistics is ru
by ww_wpg 5y ago
> You cannot calculate the EV of a random variable X by taking the mean of random samples drawn from the distribution of X
My understanding of statistics is rudimentary so forgive me but doesn't the sample mean of a normally distributed variable tend towards the expected value for the population?
- mturmon 5y agoThe sample mean of a Normal RV does tend towards the population expected value, sure. The GP comment is talking about a Cauchy RV, which has heavy tails. So it has enough probability mass at large values that the expected value is infinite. Discarding constant scale factors, in this case: E[X] = Int{0..infty} x * p(x) dx = Int{0..infty} x * (1/x^2) dx = Int{0..infty} (1/x) dx = +infty So, the sample mean of Cauchy random variates will not converge to any real number.