Statistics: Mean values

1. Jan 16, 2009

Niles

1. The problem statement, all variables and given/known data
Hi all.

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

$$<y_k^2> = \frac{1}{N}\sum_1^N{y_k^2} \quad \text{and} \quad <x_k^4> = \frac{1}{N}\sum_1^N{x_k^4}.$$

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

Question: Is it correct that:

$$<y_kx_k^2> = \sqrt{<x_k^4><y_k^2>}.$$

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.

Niles.

2. Jan 16, 2009

Staff: Mentor

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).

3. Jan 16, 2009

Niles

Yeah, just what I thought.. so they are not the same.

Thanks.