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If we increase the degree of standard deviation of one variable, does it affect covariance of two variables? Example, two variables are there, A & B, the covariance of A & B is 100, and the degree of standard deviation of A is 12, let say, if the degree of standard deviation of A is increased from 12 to 18, is there any changes in covariance of A & B? If I ask question in another way, then, if slope of A & B is 1, and degree of standard deviation of A is 12, what is new slope of A & B if degree of standard deviation of A increases from 12 to 18?

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You're making a transformation on $A$ and get another RV $X=f(A)$. This can be simple scaling or any other operation. The covariance between the newly transformed variable $X$ and $B$ will in general change, i.e. in general, we have$$\operatorname{cov}(A,B)\neq \operatorname{cov}(X,B)$$

A simple example would be scaling, $X=2A$:$$\operatorname{cov}(X,B)=\operatorname{cov}(2A,B)=2\operatorname{cov}(A,B)\neq \operatorname{cov}(A,B)$$ in general.

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