3.9.3 (Exercise 3.6.6 Continued) Suppose that (X, X) is distributed as N(3, 1, 16, 25, 3/5)....

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3.9.3 (Exercise 3.6.6 Continued) Suppose that (X₁, X₂) is distributed as N₂(3, 1, 16, 25, 3/5). (i) Use Tchebysheff's inequality to get a lower bound for P{-2 < X₂ < 10 | X₁ = 7}; (ii) Use Cauchy-Schwarz inequality to obtain an upper bound for (a) E[X,X₂] and (b) E[X²X2]. {Hint: In part (i), work with the conditional distribution of X₂ | X₁ = 7 and from X, subtract the right conditional mean so that the Tchebysheff's in- equality can be applied. In part (ii), apply the Cauchy-Schwarz inequality in a straightforward manner.} 3.9.3 (Exercise 3.6.6 Continued) Suppose that (X₁, X₂) is distributed as N₂(3, 1, 16, 25, 3/5). (i) Use Tchebysheff's inequality to get a lower bound for P{-2 < X₂ < 10 | X₁ = 7}; (ii) Use Cauchy-Schwarz inequality to obtain an upper bound for (a) E[X,X₂] and (b) E[X²X2]. {Hint: In part (i), work with the conditional distribution of X₂ | X₁ = 7 and from X, subtract the right conditional mean so that the Tchebysheff's in- equality can be applied. In part (ii), apply the Cauchy-Schwarz inequality in a straightforward manner.}