3.3.25 Suppose that (X1, X2, X3) ~ Multinomial(n, 01, 02, 03). Prove that Var(X;) = n0; (1 -0;), Cov(X;, X;) = -10;0;, wheni # j. (a) Chapter 3 Exercise 3.3.25. You can do this directly from the joint pmf, but here is a simpler alternative approach. First observe that X; ~ binomial(n, 0;) (recall Example 2.8.5 in the text) and Xi + Xj ~ binomial(n, 0; + 0;) if i # j (why? - think about combining categories). Then use that fact and properties of variance and covariance to get two expressions for Var(Xi+ Xj) which you can use to solve for the desired covariance. (b) Use the above to find Corr(Xi, X;). How does the correlation change with n