There’s a great question/answer at: Calculating probabilities over different time intervals This is an awesome answer, but I’d like to ask a related question: What if the period goes the other direction, for example, the probability is determined for a year, but you want to see the probability of it happening over 50 years? For […]

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if $X,Y\sim^{iid} (0,1)$ (which implies $E(XY)=E(X)E(Y)$), why then is it that $E(X^2Y^2)=E(X^2)E(Y^2)$? This spins-off from another question wherein apparently “If the squares were dependent, there’s […]

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