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bivariate analysis

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bivariate analysis

suppose we are given two random variables X and Y.
how can we prove the following proposition:-

If Cov(X,Y)=0 , X and Y are independent if and only if each of X and Y take oat most two distinct values.

not true. If X and Y are normally distributed, then Cov(X,Y)=0 is equivalent to independence. There may be other examples.

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