The Accompanying Table Shows the Joint Distribution Between the Change

Essay

The accompanying table shows the joint distribution between the change of the unemployment rate in an election year and the share of the candidate of the incumbent party since 1928. You think of this data as a population which you want to describe, rather than a sample from which you want to infer behavior of a larger population.
Joint Distribution of Unemployment Rate Change and Incumbent Party's Vote
Share in Total Vote Cast for the Two Major-Party Candidates,
1928-2000 $$\begin{array} { | c | c | c | c | } \hline & \begin{array} { c } ( \text { Incumbent } - 50 \% ) > 0 \\( Y = 0 )\end{array} & \begin{array} { c } ( \text { Incumbent } - 50 \% ) \leq 0 \\( Y = 1 )\end{array} & \text { Total } \\\hline \Delta u > 0 ( X = 0 ) & 0.053 & 0.211 & 0.264 \\\hline \Delta u \leq 0 ( X = 1 ) & 0.579 & 0.157 & 0.736 \\\hline \text { Total } & 0.632 & 0.368 & 1.00 \\\hline\end{array}$$ (a)Compute and interpret E(Y)and E(X).
(b)Calculate E(Y $\mid X$ = 1)and E(Y $\mid X$ = 0). Did you expect these to be very different?
(c)What is the probability that the unemployment rate decreases in an election year?
(d)Conditional on the unemployment rate decreasing, what is the probability that an incumbent will lose the election?
(e)What would the joint distribution look like under independence?