1. A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution of X

2. Bivariate U((0,1),(0,1))

3. Bivariate Normal Distribution

4. Three Senators’ Article I impeachment votes: Eight possible outcomes LottWellstoneLieberman 111 110 101 100 000 011 010 001 ProbIF p=1/4 p3p3 1/64 p 2 (1-p)3/64 p 2 (1-p)3/64 p(1-p) 2 9/64 (1-p) 3 27/64 p 2 (1-p)3/64 p(1-p) 2 9/64 p(1-p) 2 9/64 Observed

5. Bernoulli Likelihood Function, Three observation case

6. The Effect of k(y)

7. Two Extrema

8. The MLE

9. Bernoulli Likelihood and Log- likelihood, three observation case

10. Ln(exports) by country, 2001