Following Alfred Nobel's Will, There Are Five Nobel Prizes Awarded

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 $$\begin{array} { | c | c | c | c | } \hline & \begin{array} { c } \text { U.S. Citizen } \\( Y = 0 )\end{array} & \begin{array} { c } \text { Non= U.S. Citizen } \\( Y = 1 )\end{array} & \text { Total } \\\hline \begin{array} { c } \text { Economics Nobel } \\\text { Prize } ( X = 0 )\end{array} & 0.118 & 0.049 & 0.167 \\\hline \begin{array} { c } \text { Physics, Chemistry, } \\\text { Medicine, Literature, } \\\text { and Peace Nobel } \\\text { Prize } ( X = 1 )\end{array} & 0.345 & 0.488 & 0.833 \\\hline \text { Total } &0.463 &0.537 &1.00 \\\hline\end{array}$$ (a)Compute E(Y)and interpret the resulting number.
(b)Calculate and interpret E(Y $\mid X$ =1)and E(Y $\mid X$ =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.