Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines, and Citizenship, 1969-2001 U.S. Citizen Non U.S. Citizen Total (Y = 0) (Y = 1) Economics Nobel Prize (X = 0) 0.118 0.049 0.167 Phy., Chem., Med., Lit., and 0.345 0.488 0.833 Peace Nobel Prize (X = 1) Total 0.463 0.537 1.00 (a) Compute E(Y) and interpret the resulting number. (5pt) (b) Calculate and interpret E(Y|X=1) and E(Y|X=0). (5pt) (c) A randomly selected Nobel Prize winner reports that he is a non-U.S. citizen. What is the probability that this genius has won the Economics Nobel Prize? A Nobel Prize in the other five disciplines? (5pt) (d) Show what the joint distribution would look like if the two categories were independent if the marginal probabilities remain unchanged. (5pt)