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 definition about finite mean and variance. I searched on google, but seems there is no explanation in datail. Can anyone help me out? Thanks

  • $\begingroup$ 1) Kindly use the self-study tag. 2) Do you know the integral (or sum) definitions of population mean and population variance? $\endgroup$
    – Dave
    Dec 5, 2019 at 22:32
  • $\begingroup$ Search for infinite mean variance for many discussions and examples. The first duplicate addresses your confusion. The second duplicate answers the question about finite variance. The third duplicate answers the question about finite mean. $\endgroup$
    – whuber
    Dec 5, 2019 at 22:34


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