Description
Three problems:
1.19
A. Given: The components of a random vector are jointly Gaussian if the vector is
multivariate normally (MVN) distributed. Suppose that two random variables X and Y are
jointly Gaussian and satisfy cov(X, Y) = 0. It is then well known that X and Y are independent
(see any of many textbooks on probability).
Question: Now, consider the case where X is normally distributed and Y is normally
distributed and cov(X, Y) = 0. Show that X and Y are not necessarily independent. (Hint:
Consider the counterexample to MVN discussed in class lecture.)
B. Consider an LCG with c = 0, X0 = 1, and modulus, m = 13. Suppose we consider 12
possible values of a, namely a ∈ {1, 2, …, 12}. Which values of a in the set of 12
possible values will yield a generator that produces all possible outcomes Xk ∈ {1, 2, …,
12}? (Note that Xk cannot equal 0, or else the algorithm will get stuck at 0.)
