What is the Expectation of a Ratio of Independent Random Variables?

Thread starter shoplifter
Start date Nov 13, 2010
Tags

Independent Random Random variables Variables

In summary, independent random variables are variables that have no influence on each other and do not affect each other's outcomes. They are different from dependent random variables which are related and can impact each other's outcomes. In statistics, independent random variables allow for certain assumptions and simplifications in data analysis. To determine if two random variables are independent, a statistical test can be performed. Independent random variables can become dependent over time if external factors or other variables come into play.

Nov 13, 2010

shoplifter

Let x_1, x_2, ..., x_n be identically distributed independent random variables, taking values in (1, 2). If y = x_1/(x_1 + ... + x_n), then what is the expectation of y?

Physics news on Phys.org

Nov 20, 2010

bpet

Hint: use E[(x_1+...+x_n)/(x_1+...+x_n)]=1.

What are independent random variables?

Independent random variables are variables that have no influence on each other. This means that the outcome of one variable does not affect the outcome of the other.

How are independent random variables different from dependent random variables?

Dependent random variables are variables that are related to each other in some way, meaning that the outcome of one variable can impact the outcome of the other. Independent random variables, on the other hand, have no relationship and do not affect each other's outcomes.

What is the significance of independent random variables in statistics?

Independent random variables are important in statistics because they allow us to make certain assumptions and simplifications when analyzing data. For example, we can assume that the variables are normally distributed and use simpler mathematical equations to calculate probabilities.

How can you determine if two random variables are independent?

To determine if two random variables are independent, you can perform a statistical test, such as the Pearson correlation coefficient, to measure the strength of the relationship between the variables. If the correlation is close to zero, then the variables are likely independent.

Can independent random variables become dependent over time?

Yes, it is possible for independent random variables to become dependent over time. This can happen if external factors or other variables come into play that affect the outcomes of the original variables. It is important to continually evaluate the relationship between variables in statistical analysis to ensure their independence.