# Homework Help: X1X2 ~ Y1Y2 if

1. Sep 27, 2008

### shan

1. The problem statement, all variables and given/known data
If X1 ~ Y1 and X2 ~ Y2, then X1X2 ~ Y1Y2, prove or find a counterexample. (the distribution of X1 has the same distribution of Y1 etc)

2. Relevant equations
-

3. The attempt at a solution
I'm guessing the statement is true. For example if X1 and Y1 were both uniform and X2 and Y2 are binomial, then a uniform * binomial is distributed the same as a uniform * binomial.

2. Sep 27, 2008

### HallsofIvy

It would help if you also told us what "~" meant.

3. Sep 27, 2008

### shan

Ah sorry, it's the stuff I put in the brackets ie.

X1 ~ Y1 : the distribution of X1 has the same distribution of Y1, X1 and Y1 being random variables.

The same with X2 ~ Y2 and X1X2 ~ Y1Y2.

4. Oct 5, 2008

### shan

If anyone was interested, the answer was no. The counter example was:

Let $$P(X_1 = 1) = P(X_1 = -1) = 0.5$$. Let $$X_2 = -X_1$$ and $$Y_1 = Y_2 = X_1. X_1 X_2 = -X_1^2 = -1$$ almost surely, but $$Y_1 Y_2 = X_1^2 = 1$$

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