1. (5 points) Answer the following questions with a very briey justication. (a) Four mutually exclusive events A, B , C, D each have a probability of 0.25. What is the proba bility that two or more of them will occur? (b) Is it true that a continuous RV must have a continuous PDF? Can it include delta functions? (c) Given two zeromean Gaussian RVs X and Y with variances 0:20 > 05,, which one has a higher probability of taking on values that are small in magnitude? ((1) Are RVs X and Y always uncorrelated if their joint CDF is equal to the product of their marginal CDFs? (e) For two RVs X and Y, is it always true that var(X) 2 var(Y) if E [X] 2 E [Y]