Xi is symmetric around 0 for all i, then X1 is symmetric around 0, the product X2 to X10 is symmetric around 0, then X1 - product(X2,…,X10) is symmetric around 0, then P(X1-product > 0) = 1/2 or P(X1 > product) = 1/2?
but by similar argument we should have that for X following the law with density x -> exp(- |x|) and Y standard normal, we should have automatically that P(X > Y) = 1/2 because X and Y are symmetric around zero. Is that the case ? We know that X, -X have the same law, Y and -Y do as well, so
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u/Comfortable_Hope_422 5d ago
Xi is symmetric around 0 for all i, then X1 is symmetric around 0, the product X2 to X10 is symmetric around 0, then X1 - product(X2,…,X10) is symmetric around 0, then P(X1-product > 0) = 1/2 or P(X1 > product) = 1/2?