Probability question that I just can't solve.

[datatec]

Hi,

My formal mathematical training is minimal and it is for this reason that I tend to deal with these types of problems on a highly intuitive and abstract level, please therefore forgive my clear ignorance both respect to the way I describe this problem and the fact that I can't find a solution for it.

We have two positively correlated variables (I suppose the best way to illustrate this fact is with a correlation coefficient of say 0.7; would I be right in supposing this?) furthermore both variables have a standard normal distribution. My question is, suppose these two variables fluctuate over time and in the first period variable A moves 1 s.d. higher it must follow that variable B's mean is no longer 0 but rather another value (is this correct?).

Any help will be much appreciated.

Thank you all.

 

[EnumaElish]

Correlation is independent of the location, so no.

http://en.wikipedia.org/wiki/Correlation

 

[tacman]

Hello,

Thank you for reaching out with your question. It sounds like you are dealing with a problem involving two correlated standard normal variables. To answer your question, yes, if one variable (let's call it A) moves 1 standard deviation higher, then the mean of the other variable (B) will also change. This is because the mean of B is dependent on the value of A. The exact value of B's mean will depend on the strength of the correlation between the two variables.

To find the new mean of B, you can use the formula: new mean of B = correlation coefficient * (1 standard deviation increase in A). In your case, with a correlation coefficient of 0.7 and a 1 standard deviation increase in A, the new mean of B would be 0.7.

I hope this helps. If you have any further questions or need clarification, please don't hesitate to ask. Best of luck with your problem!