Hi, this might be very easy but I am unable to prove it.
(From now on, the summations will be defined over the set {R,P,M})
Let ; where
and and
and
and also, define
Now the claim is:
1) If ; then
2) If ; then
Alpha's being in between 0 and 1 and summing to 1 seems to be crucial for this fact, since I tried around 50 examples in excel and it holds if thats the case.
Any help is appreciated.
p.s. forgot to add, we also have
edit: I got it, it's not tricky at all actually. If anyone's interested, just post a reply here and I'll write the solution.