3.3 Let X denote the change in the number of international confrontations into which a nation entered from the quarter century preceding World War II to the quarter century following World War II; let Y denote the change in the gold reserves of a nation over the same two time periods. Suppose where Find: E(Y|X), E(X|Y), var (Y|X), var (X|Y), P{X ≤ 6}, P{4 ≤ X ≤ 6, 1 ≤ Y ≤ 3}. [Hint: For part (d), see, for example, the tables in Owen, 1962.]