E[min (t, sigma y(i))] >= Sigma [q(i)/p(i)]
or in other words
E[min (t,i1+i2+i3+.........+in)*Pr(i1)Pr(i2)...........P r(in)]
i1,i2,i3,,,,,,,in goes from 1 to infinity
where y is a random variable following geometric distribution.
Is there a way to find a lower bound for t which would make the computation much easier.
Even for the case of i=2 i.e. y1+y2 the computation gets huge. Let alone for solving for a general n here. We have the input of