Following Alfred Nobel's will, there are five Nobel Prizes awarded each year. These are for outstanding achievements in Chemistry, Physics, Physiology or Medicine, Literature, and Peace

In 1968, the Bank of Sweden added a prize in Economic Sciences in memory of Alfred Nobel. You think of the data as describing a population, rather than a sample from which you want to infer behavior of a larger population. The accompanying table lists the joint probability distribution between recipients in economics and the other five prizes, and the citizenship of the recipients, based on the 1969-2001 period.

Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines, and Citizenship, 1969-2001

U.S. Citizen
(Y = 0) Non= U.S. Citizen
(Y = 1) Total
Economics Nobel Prize (X = 0) 0.118 0.049 0.167
Physics, Chemistry, Medicine, Literature, and Peace Nobel Prize (X = 1) 0.345 0.488 0.833
Total 0.463 0.537 1.00

(a) Compute E(Y) and interpret the resulting number.
(b) Calculate and interpret E(Y =1) and E(Y =0).
(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?
(d) Show what the joint distribution would look like if the two categories were independent.
What will be an ideal response?

Answer:
(a) E(Y) = 0.53.7 . 53.7 percent of Nobel Prize winners were non-U.S. citizens.
(b) E(Y =1) = 0.586 . 58.6 percent of Nobel Prize winners in non-economics disciplines were non-U.S. citizens. E(Y =0) = 0.293 . 29.3 percent of the Economics Nobel Prize winners were non-U.S. citizens.
(c) There is a 9.1 percent chance that he has won the Economics Nobel Prize, and a 90.9 percent chance that he has won a Nobel Prize in one of the other five disciplines.
(d)
Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines,
and Citizenship, 1969-2001, under assumption of independence

U.S. Citizen
(Y = 0) Non= U.S. Citizen
(Y = 1) Total
Economics Nobel Prize (X = 0) 0.077 0.090 0.167
Physics, Chemistry, Medicine, Literature, and Peace Nobel Prize (X = 1) 0.386 0.447 0.833
Total 0.463 0.537 1.00