- #1
robertdeniro
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Homework Statement
if X and Y are independent random variables
does it imply that X^2 and Y^2 are also independent?
Probability independent variable question
- Thread starter robertdeniro
- Start date
In summary, the conversation discusses whether or not the independence of two random variables, X and Y, implies the independence of their squared values, X^2 and Y^2. The initial attempt at a solution suggests using the fact that E(XY)=E(X)E(Y) to show that E(X^2Y^2) = E(X^2)E(Y^2). However, it is pointed out that this approach is incorrect and that independence must be proven using probabilities, not expectation values. The conversation ends with a suggestion to find a proof that involves probabilities instead.
if X and Y are independent random variables
does it imply that X^2 and Y^2 are also independent?
- #2
tiny-tim
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hi robertdeniro! 
(try using the X2 tag just above the Reply box)
Tel us what you think, and why, and then we'll comment!
(try using the X2 tag just above the Reply box
)Tel us what you think, and why, and then we'll comment!
- #3
robertdeniro
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i think X2 and Y2 are also independent because
E(XY)=E(X)E(Y)
so E(X2Y2)=E(X2)E(Y2) ?
E(XY)=E(X)E(Y)
so E(X2Y2)=E(X2)E(Y2) ?
- #4
tiny-tim
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robertdeniro said:
Nooo
… why would E(AB) = E(A)E(B)? You must prove independence by considering probabilities, not expectation values …
find a proof that involves P, not E.
FAQ: Probability independent variable question
What is a probability independent variable?
A probability independent variable is a variable that does not depend on any other variables in a probability distribution. It has no impact on the outcome of the event being studied and can be varied freely without affecting the results.
How is a probability independent variable different from a dependent variable?
A probability independent variable is not affected by any other variables in a probability distribution, while a dependent variable is influenced by at least one other variable. The value of a dependent variable changes depending on the value of the independent variable.
Can you give an example of a probability independent variable?
One example of a probability independent variable is the flip of a coin. The outcome of one coin flip does not affect the outcome of the next flip, making it a probability independent variable.
How do you calculate the probability of an independent variable?
The probability of an independent variable can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a 3 on a fair six-sided die is 1/6, since there is only one way to roll a 3 and six possible outcomes in total.
What is the relationship between probability independent variables and statistical independence?
Probability independent variables and statistical independence are closely related concepts. If two variables are statistically independent, it means that they have no correlation with each other. In other words, the value of one variable does not affect the value of the other. This also means that they are probability independent variables, as the value of one does not impact the probability of the other.