Advertisements claim that taking an SAT preparation course can slgnli'icantlv Improve performance on the SAT. Assume there are three SAT preparation services available for students to enroll In, and assume you have zoo students available to use In your experiment. Explain the design of an experiment to examine the claim that SAT preparation courses improve SAT scores and, If so, which of the preparation services would seem to be the best. [15 points}' 8. Suppose that X and Y have a bivariate normal distribution with Var[X ] = 1, Var[Y] = 2, E[X] = 3, E[Y] = 7, and pxy = 0.5. Compute the following. Hint: Use Equation 5.22, definition of correlation, and the properties of conditional distributions of normal random variables. This should only take a minute to finish!. . E[X2] . Cov[X, Y] . EY|X] when X = 3 . Var[X|Y] when Y = 1Consider the following Markov chain with the following transition diagram on states {1, 2, 3} al- 2 CO 173 3 (a) Is this Markov chain irreducible? [1 marks] (b) Find the probability of the Markov chain to move to state 3 after two time steps, providing it starts in state 2. [3 marks]Let {Xiji=1 36 be the sequence of continuous IIDRV with EXi = 40, Var Xi = 144, i = 1, ..., 36 and A36 Eil Xi = 36 (a) By using the Markov's inequality estimate P( A36