There are frequently situations where you have information on the ...

[sheilaspns]

There are frequently situations where you have information on the conditional distribution of Y given X, but are interested in the conditional distribution of X given Y.
 
  Recalling Pr(Y = y = x) = , derive a relationship between Pr(X = x = y) and Pr(Y = y = x). This is called Bayes' theorem.
  What will be an ideal response?

Question 2

Correlation of the regression error across observations
 
  A) results in incorrect OLS standard errors.
  B) makes the OLS estimator inconsistent, but not unbiased.
  C) results in correct OLS standard errors if heteroskedasticity-robust standard errors are used.
  D) is not a problem in cross-sections since the data can always be reshuffled.

[Galvarado142]

Answer to Question 1

Answer:
Given Pr(Y = y = x) = ,
Pr(Y = y = x)  Pr(X = x) = Pr(X = x, Y = y);
similarly Pr(X = x = y) = and
Pr(X = x = y)  Pr(Y = y) = Pr(X = x, Y = y). Equating the two and solving for Pr(X = x = y) then results in
Pr(X = x = y) = .

Answer to Question 2

Answer: A