Hello,

I would like your help!

X1, X2, … are independent continuous random variables with E[x]=2, V(X)=9.

Yi=(0.5^i)Xi, i=1,2,…

Tn=Y1+Y2+…+Yn

An=(1/n) Tn

E and V of Yn, Tn, An ???

E[Yn] = E[(0.5^i)Xi] = (0.5^i)E[Xi] = 2(0.5^i)

V[Yn] = V[(0.5^i)Xi] = [(0.5^i)^2] V[Xi] = 9 [(0.5^i)^2]