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

Thread starter zli034
Start date Apr 2, 2010
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In summary, the product of expectations in statistics refers to the expected value of the product of two random variables, calculated by multiplying their expected values. It is commonly used in data analysis and research to make predictions and draw conclusions, taking into account the interaction between the two variables. It differs from the sum of expectations, which only adds the expected values of the two variables. The product of expectations can be negative and is related to other statistical measures such as covariance and correlation. It is also used in the calculation of the variance of a function of two variables.

Apr 2, 2010

zli034

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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Apr 3, 2010

mathman

Science Advisor

Only if x and y are independent. If not, anything can happen - simple example y=x.

Apr 3, 2010

zli034

cool

1. What is the definition of "product of expectations" in statistics?

The product of expectations is a statistical concept that refers to the expected value of the product of two random variables. It is calculated by multiplying the expected values of the two variables.

2. How is the product of expectations used in data analysis and research?

The product of expectations is often used to calculate the expected value of a function of two variables, which can then be used to make predictions or draw conclusions in research and data analysis.

3. How is the product of expectations different from the sum of expectations?

The product of expectations is calculated by multiplying the expected values of two variables, while the sum of expectations is calculated by adding the expected values of two variables. This means that the product of expectations takes into account the interaction between the two variables, while the sum of expectations does not.

4. Can the product of expectations be negative?

Yes, the product of expectations can be negative. This can occur when one variable has a positive expected value and the other has a negative expected value, or when both variables have negative expected values but their product is positive.

5. How is the product of expectations related to other statistical measures?

The product of expectations is related to other statistical measures, such as covariance and correlation, as it involves the interaction between two variables. It is also used in the calculation of the variance of a function of two variables.