finding UMVUE of parameter 1/(1+λ)

#1
suppose X1,X2,X3 are a random sample of exponential distribution with parameter λ. how can i find UMVUE parameter 1/(1+λ). note: (T=∑Xi,(i=1,2,3); f(x)=λexp(−λx)).
I know that T= X1+X2+X3 is the minimal sufficient statistic and is complete and
that i want g(t), where ∫_0^∞(g(t))((λ^3)/2) (t^2).(e^(-λt)) dt=1/(1+λ) but i don't know that how i can find g(t)? please guide me
 

Dason

Ambassador to the humans
#2
Can you find a simpler statistic that isn't a function of T that has an expectation of 1/(1+lambda)?