Word Count : 214

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For the probability density function (f(x) = \theta e^{-\theta x}), (x \ge 0), (\theta > 0), we calculate the expected value (E(X)) and variance (V(X)) manually. Step 1: Expected value (E(X)) [ E(X) = \int_0^\infty x f(x) , dx = \int_0^\infty x \theta e^{-\theta x} , dx ] Use integration by parts: let ________ ___ ____ __________ ________ _________.
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