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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

Ryan Zhou
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  • 1) Kindly use the self-study tag. 2) Do you know the integral (or sum) definitions of population mean and population variance? – Dave Dec 05 '19 at 22:32
  • Search for [infinite mean variance](https://stats.stackexchange.com/search?q=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. – whuber Dec 05 '19 at 22:34

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