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 X∼Bin(n,0.5) and Y∼Bin(n+1,0.5).
P(X<Y)=P(n−X<n+1−Y), since the probability distribution of Bin(n,0.5) and n−X should be exactly the same.
Thanks in advance for your help!
No comments:
Post a Comment