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I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is $$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$ but, how do I derive it from "common" rules of variance calculations?

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    What makes you say that is the solution?2011-05-22
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    $\var(X-Y) = \var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y)$ and not $\var(X/Y)$2011-05-22
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    Sanity check your formula for $Y=X$, then your formula should vanish which is not the case here.2011-05-22
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    Cardinal: It gives the correct answer, and that formula was used in a video feed I saw. I just want to understand how to derive it.2011-05-22
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    Listing: If Y = X, we should have var(X) + var(X) - 2var(X)*1 = 0?2011-05-22
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    @Tomas: Try plugging in $X=0$ in the formula you have, to realize it is not true2011-05-22
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    Thomas no at the right side you have $2 \var(X)^2$ which is in the general case not equal to $2 \var(X)$2011-05-22
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    Don't believe everything which you see in a video feed!2011-05-22
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    Strictly $\var(X−Y)=\var(X) + \var(Y) - 2 \sqrt{\var(X) \var(Y)} \mathrm{corr}(X,Y)$. Otherwise there is a dimension problem.2011-05-22
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    The note given in the link below explains the topic nicely http://www.stat.cmu.edu/~hseltman/files/ratio.pdf2015-06-14

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