Probability question that I just can't solve.

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SUMMARY

This discussion centers on the relationship between two positively correlated variables, specifically with a correlation coefficient of 0.7, both following a standard normal distribution. The user inquires whether an increase of one standard deviation in variable A affects the mean of variable B. The consensus is that correlation does not influence the mean location of the variables, affirming that the mean of variable B remains at 0 despite fluctuations in variable A.

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  • Understanding of correlation coefficients, specifically 0.7 correlation.
  • Knowledge of standard normal distribution concepts.
  • Familiarity with statistical terminology related to mean and standard deviation.
  • Basic grasp of how variables interact in statistical contexts.
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  • Study the implications of correlation coefficients on variable relationships.
  • Learn about the properties of standard normal distributions in depth.
  • Research the concept of conditional expectations in statistics.
  • Explore the effects of variable fluctuations on statistical means.
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Statisticians, data analysts, and students studying probability and correlation in statistics will benefit from this discussion.

datatec
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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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