The formula for the expected value of a continuous random variable is [itex]E(x) = \int_{-\infty}^{\infty} x\cdot f(x)[/itex]. This leads me to believe that the expected value of a function g(x) is [itex]E(x) = \int_{-\infty}^{\infty} g(x)\cdot f(g(x))[/itex]. However, the correct formula is [itex]E(x) = \int_{-\infty}^{\infty} g(x)\cdot f(x)[/itex]. Why is this?(adsbygoogle = window.adsbygoogle || []).push({});

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# Formula for the expected value of a function

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