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November 18th, 2016, 10:39 PM   #1
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How to find expectation of a continuous random variable by using indicator?

Let's take a simple example. X ~ Uniform [0,2]. We know E(X) is 1 using the standard formula. But how to find this using indicator function?
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November 19th, 2016, 02:46 PM   #2
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In general, you need to integrate the indicator function to get a normalization factor. Divide the indicator by this factor and you have the density function.
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