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Question: Trying to get the absolute difference between two random variables

Question:Trying to get the absolute difference between two random variables

JoyDivisionMan 50 Maple 2023
probability-function statistics
2 hours ago
0

I have a random variable called Y1, which looks like the following: Y1 = 2*sqrt(1 - x^2)/Pi, on the (-1 < x < 1) interval. This "semicircle" integrates to 1, like other random variables. Random variable Y2 is the same as Y1 above. I want to find the random variable Z, which is equal to the absolute difference of two random variables Y1 and Y2. In other words, I want to find Z = |Y1 - Y2|. Via simulation, I know that |Y1 - Y2| takes on a logrithmic form, but I need to get a mathematical solution of this.
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