X denotes government will increase payment. x~Bin(2,2/3) . if one increment =9%. expected increment =? If Government increases payment then they increase it by 9% . now if whether government will increase payment follows binomial distribution with parameters n=2 and p=(2/3) , then what percentage of payment increase is expected ? my logic is let X denotes government will increase payment. then x follows Bin(2, 2/3) then E(X)=4/3. so expected payment increase is 9*(4/3)=12%

That's correct if, in the case of two increases, the dollar amounts in both increases are the same. But I suspect you need to use compound interest.

So the first increase is $9\%$. The second increase is $9\%\times 1.09 = 9.81\%$. This makes a total percentage increase of $ 9\% + 9.81\% = 18.81\%$.

So

$$E(X) = 9\%\times \binom{2}{1}\dfrac{2}{3}\dfrac{1}{3} + 18.81\%\times \binom{2}{2}\left(\dfrac{2}{3}\right)^2 = 12.81\%.$$