<p><span class="math-container">$$E\left[\frac{(y-\mu)^2}{\sigma^2}\right] $$</span></p>
<p><span class="math-container">$\sigma^2$</span> is a constant,</p>
<p><span class="math-container">$$\frac{1}{\sigma^2}E\left[(y-\mu)^2\right] $$</span></p>
<p>I assume <span class="math-container">$\sigma^2$</span> is notation for the variance of <span class="math-container">$y$</span>, and thus <span class="math-container">$Var(y) = \sigma^2 = E\left[(y-\mu)^2\right]$</span>.</p>
<p>We now have,</p>
<p><span class="math-container">$$\frac{1}{\sigma^2}\sigma^2 =1 $$</span></p>

CC BY-SA 4.0
2022-10-31T09:32:49.107Z
Thank you very much for this fast reply and solution :)
Sera
CC BY-SA 4.0
2022-10-31T19:18:52.623Z
@Sera if you found this answer useful, I suggest you to accept it (i.e. to click on the checkmark.)
Amelian
CC BY-SA 4.0
2022-10-31T09:29:54.363Z
2022-10-31T09:29:54.363Z
Michael Gmeiner
<p>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.</p>
<p><a href="https://i.sstatic.net/jQCOt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/jQCOt.png" alt="enter image description here" /></a></p>

<econometrics><statistics>
Expected Value / Econometrics
Sera
# Expected Value / Econometrics

(Asked by: username_0 on 2022-10-31)

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.

[![enter image description here](https://i.sstatic.net/jQCOt.png)](https://i.sstatic.net/jQCOt.png)

**Tags:** econometrics, statistics

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## 1 answers

### Answer by username_1 on 2022-10-31. Score: 3 | Accepted answer

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

$\sigma^2$ 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,

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

> **Comments:**
> **username_0**: Thank you very much for this fast reply and solution :)  
> **username_2**: @Sera if you found this answer useful, I suggest you to accept it (i.e. to click on the checkmark.)  

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