Probability question that I just can't solve.

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The discussion revolves around understanding the implications of a correlation coefficient of 0.7 between two positively correlated variables that follow a standard normal distribution. The user questions whether an increase of one standard deviation in variable A affects the mean of variable B. Responses clarify that correlation does not change the mean of the variables; it only indicates the strength and direction of their relationship. The concept of correlation being independent of location is emphasized, reinforcing that the mean remains at zero despite fluctuations. Overall, the user seeks clarity on the relationship between correlated variables and their statistical properties.
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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.
 
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