YOU mean Yi not Yn
Then sum to get Tn, which is a partial geometric sum from calc 2.
I would like your help!
X1, X2, … are independent continuous random variables with E[x]=2, V(X)=9.
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]
Is the following solution correct ?
E(Tn) = E(Y1)+E(Y2)+…+E(Yn) = 2*SUM(0.5^n)
V(Tn) = V(Y1)+V(Y2)+…+V(Yn)= 9*SUM((0.5^n)^2)
E(An)=E((1/n)* Tn)= 1/n *E(Tn) = 2/n* SUM(0.5^n)
V(An)= V((1/n)* Tn) =(1/n)^2 *V(Tn) = ((1/n)^2 )*(9*SUM((0.5^n)^2))