Let X N0 1 and Y X2 Compute CovX Y and Cor X Y In this pro

Let X ~ N(0, 1) and Y = X^2. Compute Cov(X, Y) and Cor (X, Y). In this problem, Y completely depends on X, but your (correct) calculation shows that Cor(X, Y) is zero. Therefore this example shows zero correlation does not always imply independence, although independent random variables have zero correlation (or we say they are uncorrelated). Can you provide another example of two dependent random variables whose correlation is zero?

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