a) On the throw of a fair die, the expected value of the numbershowing is 3.5 and the standard deviation is 1.71. What is theexpected value and standard deviation of the sum of the values fromthe throw of a pair of dice
b) Suppose Y1 and Y2 are independent,Var(Y1) = Var(Y2) = σy2and Z1 = Y1+Y2 .What isVar(Z1)? How does this compare to the result found inpart a)?
c) Generalize the previous results. Suppose Y1,Y2, · · · , Yn are independent,Var(Y1) = Var(Y2) = · · · =Var(Yn) = σ2y and Z2 =Y1 + Y2 + · · · + Yn. What isVar(Z2)?
d) Again, let’s keep generalizing these results. SupposeY1, Y2, · · · , Yn areindependent, Var(Y1) = Var(Y2) = · · · =Var(Yn) = σ2y and Z3 =1/n (Y1 + Y2 + · · · + Yn). Whatis Var(Z3)?
