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I would like to learn how the expression below is 1. Without understanding it I am having trouble to go on with Chebbyshev's Inequality. It's maybe too basic, but I appreciate any help.

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$$E\left[\frac{(y-\mu)^2}{\sigma^2}\right] $$

$\sigma^2$ is a constant,

$$\frac{1}{\sigma^2}E\left[(y-\mu)^2\right] $$

I assume $\sigma^2$ is notation for the variance of $y$, and thus $Var(y) = \sigma^2 = E\left[(y-\mu)^2\right]$.

We now have,

$$\frac{1}{\sigma^2}\sigma^2 =1 $$

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  • $\begingroup$ Thank you very much for this fast reply and solution :) $\endgroup$
    – Sera
    Commented Oct 31, 2022 at 9:32
  • $\begingroup$ @Sera if you found this answer useful, I suggest you to accept it (i.e. to click on the checkmark.) $\endgroup$
    – Amelian
    Commented Oct 31, 2022 at 19:18

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