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I have a probability proof question that is driving me crazy. I feel

like I must have forgot an easy trick. Any help is GREATLY

appreciated. Here's the setup:

Let's assume a,b are indepedent random variables from cummulative

distribution F.

I think it's safe to say:

P( a > b) = .5

Now, let's assume x,y are independent random variables from CDF G.

Again:

P(x > y) = 0.5

Assume CDFs G and F are indepedent. Now it seems straightforward that:

P(x + a > y + b) = 0.5

but I don't know how to show it without assuming a distribution type.

Again, any help is appreciated.

Thank you,

Chris

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# Probability proof question

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