1 TA office hours

1. Will meet on their webex meeting places.

2. Hao Lu, luh6@, 2pm Tues and 3pm Sat.

3. Hanjing Wang, wangh36@, 3pm Fri and 9pm Sun.

4. If no one has joined in 15 minutes, they will leave.

5. Write them for other meeting times.

2 Homework 6

is on gradescope.

3 Chapter 5, Two Random Variables

1. One experiment might produce two r.v. E.g.,

   1. Shoot an arrow; it lands at (x,y).

   2. Toss two dice.

   3. Measure the height and weight of people.

   4. Measure the voltage of a signal at several times.

2. The definitions for pmf, pdf and cdf are reasonable extensions of one r.v.

3. The math is messier.

4. The two r.v. may be *dependent* and *correlated*.

5. The *correlation coefficient*, $\rho$, is a dimensionless measure of linear dependence. $-1\le\rho\le1$.

6. $\rho$ may be 0 when the variables have a nonlinear dependent relation.

7. Integrating (or summing) out one variable gives a marginal distribution.

8. We'll do some simple examples:

   1. Toss two 4-sided dice.

   2. Toss two 4-sided ''loaded'' dice. The marginal pmfs are uniform.

   3. Pick a point uniformly in a square.

   4. Pick a point uniformly in a triangle. x and y are now dependent.

9. The big example is a 2 variable normal distribution.

   1. The pdf is messier.

   2. It looks elliptical unless $\rho$=0.

10. I finished the class with a high level overview of Chapter 5, w/o any math.

4 Comic

Conditional Risk