Thread: statistics

Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
i) Find the expected value of Y and the variance of Y
ii) Find a function of Y that is asymptotically standard normal.

Originally Posted by trukka

Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
i) Find the expected value of Y and the variance of Y
ii) Find a function of Y that is asymptotically standard normal.

E(Y) = n/2

Originally Posted by trukka

Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
i) Find the expected value of Y and the variance of Y
ii) Find a function of Y that is asymptotically standard normal.

(i) You should know that:

E(Y) = E(X1) + E(X2) + ..... + E(Xn)

Var(Y) = Var(X1) + Var(X2) + ...... Var(Xn)


(ii) The Central Limit Theorem is your friend.