(2. Let Y : 171(2) with Y N N(,u,cr). Suppose the distribution of a predictor of a new value of Y follows a normal distribution , i.e. F0 ~ N(_u, 1.23 where a is a vector of constants and 2: is the variance covariance matrix of Y. (We assume that Y0 : AIY, a linear combination of Y : (Y1,Y2,...,Yn)r.) In addition suppose Y0 = 1511(20). Find the unbiased predictor of Z0. (1. Suppose Y = (Y(3 1), ..',Y{s")t represent ozone observations in ppm at spatial locations 51,...,s ' Assume n. that Y N NE (p1,:72V), where V is matrix of known constants that can be constructed using a covariance in function , for example , C(h) : c:1 e E, where 01,0! are known parameters, and h. is the Euclidean distance for the spatial locations .91, . . . , 5\". Find the Fisher information matrix for the parameters ,1; and 0'3 for this model. e. In each of the following situations calculate the pvalue of the observed data: 1. For testing HO : 0 = % against Ha :19 > iwhen 7 successes are observed out of 10 Bernoulli trials . 2. For testing Ha : A = 1 against Ha : A > 1, when X = 3 are observed, where X N Poisson). 3. For testing H0 : A = 1 against Ha : A > 1, when X1 = 3,X = 5, and X3 = 1 are observed, where X N Poisson)