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### Is it possible for an expected value not to exist? [duplicate]

A probability density family for $x\in\mathbb{R}$ is $$f(x) = k(\theta)\left[1 + (x/\theta)^2\right]^{-1}$$ parameterized by $\theta \gt 0$. I am supposed to find $k(\theta)$ and then both $E(X)$ ...
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### Finite Mean and Finite Variance [duplicate]

Let $X$ be a random variable. Suppose there exists a constant $c ∈ R$ such that $E(|X − c|^2) < ∞$. Show that the random variable $X$ has finite mean and variance. And I'm quite confused about the ...
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### What happens when you try to find standard deviation of a (non-truncated) cauchy distribution? [duplicate]

I have read that this doesn't work, but I do not understand exactly why. Please can someone explain.
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### Does expected value of square of a random variable always exist? [duplicate]

Can we verify if $E(X^2)$ also exist, provided that E(X) exists? Thanks.
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### How to calculate the variance of the Item Count Technique (aka Unmatched Count Technique) double list?

The Item Count Technique (ITC) (aka Unmatched Count Technique) is a survey technique to ask a sensitive question while taking account to the anonymity of the respondent's answer. Therefore in standard ...