Question: Consider two identically distributed and independent random variables (X_{1}) and (X_{2}) with common probability density function (p_{X}(x)). Show that the probability density function of the

Consider two identically distributed and independent random variables $X_{1}$ and $X_{2}$ with common probability density function $p_{X}(x)$. Show that the probability density function of the difference of these two random variables, $X_{1}-X_{2}$, is given by the autocorrelation function of $p_{X}(x)$.

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