3. { Unbiased Estimator U3. Consistent Estimator) Suppose that we observe a set of i.i.d. random variables X1, ..., X\" and another set of i.i.d. random variables Y1, ..., Yn. Let us assume that the correlation between X; and K- is not zero and unknown for any i = 1, ...,n, but the correlation between X3- and 1'} for any 1' a j is zero. Suppose that our parameter of interest is as follows: 6 = EXlEYl. (a) Show that an estimator dened by 3 = fin?\" for X = i 21:21 X1- and Y' = 1132:; Y;- is a consistent estimator of 6'. (Hint: apply the Law of Large Numbers and Slutsky Theorem) (b) Show that 9 = Kn?\" is not an unbiased estimator. ((3) Provide an unbiased estimator of 6. (Hint: what is an unbiased estimator of 6 when n = 2?)