Hi all -
I have two independent (but not necessarily identically distributed) random variables: 𝑋>0,𝑌>0. All of their moments are known but we don't know the distributions.
Can we find an upper bound for 𝐸[𝑚𝑖𝑛(𝑋,𝑌)] that is better than 𝑚𝑖𝑛(𝐸[𝑋],𝐸[𝑌]) with the information given without knowing the distributions? Thanks for your help!