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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Example(s) where replacing a multivariate, discrete RV with a single, univariate RV fail

Let $X_1,\ldots,X_n,Y,Z$ be $n+2$ binary random variables and define $X=(X_1,\ldots,X_n)$. In most problems, instead of treating $X$ as $n$ distinct binary random variables, there is no loss of genera …