1. Consider the bivariate linear regression model y = B1+ Box + E, where & is independently and identically distributed as a normal random variable with mean 0 and variance oz = 4. From a random sample of size 22, you estimate 32 = 2.18. In the sample, (XX) = 0.158 -.024 -.024 0.005 You want to consider the likelihood that the following hypothesis is valid: Ho : B2 = 2. Under the null hypothesis, what is the probability that a random sample of size 22 would yield an estimated value of 8, greater than or equal to 2.18? Consult the attached Standard Normal Cumulative Probability table to answer the question. Why don't you need tables of the t-distribution to answer this question?2. You want to estimate the following very simple time series regression model: 1/t = B1+ Bat + Et, where et is independently and identically distributed (over time) with mean 0 and variance o2. You have access to a sample of observations {},. Define the XT matrix and Yr vector 1/2 XT = YT UT- 1 The Ordinary Least Squares estimator of 8 from our sample of size T is BT = (X,Xr)'X,Yr. (a) Is By an unbiased estimator of B, that is, is E(By(Xr) = B for all XT? (b) Is By a consistent estimator of 8, that is, is plim Br = 8? (c) Consider the following implication of the model. The difference between two successive values of y is given by 1/1 - 31-1 = (81 + B2t + EL) - (B1 + B2(t -1)+ 51-1) = B2 + (81 - 51-1). Define the following estimator of 8, (only 82 can be estimated, since 8, drops out in the differenceing) E(v - yt-1) By-1 = T- 1 Is By_1 an unbiased estimator of B2? (d) Is the estimator By_1 a consistent estimator of B2?3. Consider the linear regression model y = XB+E, where E(EX) = 0 and E(Es'(X) = V, and where V is a known diagonal matrix with unequal elements. (a) Define B = (X'X) 'X'y. Is E(BIX) = B? (b) Find the covariance matrix of B. (c) Is B the Best Linear Unbiased Estimator of B? If not, what is