4. The following table gives the joint probability distribution between post-graduation plans and college major among recent University of Delaware graduates who have nalized their post-graduation plans {i.e., students who are still seeking employment are not included in the table). Use the table to answer the following questions. No further education (Y=D) Further education (Y=l] Non-Lemar Grad {X=O) 0.477 E_ 0.760 Lerner Grad (10:1) 0.210 0.030 0.240 Total 0.037 0.313 1.000 (a) Compute E(X) and EO'). Explain your ndings in words. 1 (1}) Calculate E(Y|X = 1) and E(X|Y = 0). What do these mean in words? (0) What is the distribution of X conditional on Y = 0? (d) A randomly,r selected member of this population reports pursuing further educa- tion. \"that is the probability that this person is a Lerner graduate? How does this compare to the overall probability that someone is a Lerner graduate? (e) What is the probability someone is not pursuing further education given theyr are a Lerner graduate? How does this compare to the overall probability that someone is not pursuing further education? {1'} Are college major and post-graduation plans independent