Thursday, 30 March 2017

probability - Is mathbbP(X>Y)=mathbbP(X+k>Y+k) true, where X and Y are random variables?

My intuition tells me that P(X+k>Y+k)=P(X>Y) should be true, since there (should?) be a bijection between every single result between these two probability distributions. But clearly there's a misunderstanding somewhere here, but I'm having trouble pinning it down.




A counterexample would be:
Suppose XBin(n,0.5) and YBin(n+1,0.5).
P(X<Y)=P(nX<n+1Y), since the probability distribution of Bin(n,0.5) and nX should be exactly the same.



Thanks in advance for your help!

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...