Can E(y/x) be determined if E(1/x) and E(y) are known?

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E(y/x) can only be determined as b/a if x and y are independent random variables. If they are not independent, the relationship between E(1/x) and E(y) does not guarantee that E(y/x) equals b/a. An example provided illustrates that if y is directly related to x, such as y=x, the calculation would not hold. Therefore, independence is a crucial factor in determining E(y/x) from the given expectations. Understanding the dependency between variables is essential for accurate calculations in probability.
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say, E(1/x)=a and E(y)=b. a and b are constants and x and y are random variables.

Can I say E(y/x)=b/a? Thanks.
 
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Only if x and y are independent. If not, anything can happen - simple example y=x.
 
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Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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