Does it hold true that the expectation for a random variable with density is finite? I'm guessing not be would like to see an example.
Expectation for random variables with density
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probability
2 Answers
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Cauchy distribution has a density function $f(x)=\dfrac{1}{\pi}\cdot\dfrac{1}{1+x^2}$ but the expectation does not exist.
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No. Consider for instance a random variable having pdf $f(x)=\frac{1}{x^2}$ for $x\geq 1$.