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How do you calculate the variance of a piecewise function? For example, what would be the variance of the probability density function $f_x(x)= \frac{3}{4}, 0\leq x\leq 1; \frac{1}{4}, 2\leq x \leq 3; 0$ otherwise?

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    The ordinary way, you integrate, find say $\int_0^3 x^2f(x)\,dx$, subtract the square of $\int_0^3 xf(x)\,dx$. Now when you are *doing* the integrations, you have to break them up, $0$ to $1$, and $2$ to $3$.2012-03-13

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