Are the Mean Values of Two Variables Related by a Square Root?

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Homework Statement


Hi all.

Lets say I have two variables yk and xk. I also have two mean values given by:

<br /> &lt;y_k^2&gt; = \frac{1}{N}\sum_1^N{y_k^2} \quad \text{and} \quad &lt;x_k^4&gt; = \frac{1}{N}\sum_1^N{x_k^4}.<br />

Now I am looking at the expression (<xk4> <yk2>)1/2.

Question: Is it correct that:

<br /> &lt;y_kx_k^2&gt; = \sqrt{&lt;x_k^4&gt;&lt;y_k^2&gt;}.<br />

Personally, I don't think so, because ultimately it would mean that I would have to make two sums into one sum, which I can't.. but I am in doubt.

Thanks in advance.

Niles.
 
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Per your notation (< ... >), <yk2> denotes the mean of the squared values of yk.

So <xk4yk2> would be the sum of the products of xk4yk2, divided by N, which is not the same as (<xk4> <yk2>)1/2.
The latter would just be the square root of (the mean of the x^4 terms times the mean of the y^2 terms).
 
Yeah, just what I thought.. so they are not the same.

Thanks.
 
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