Week | Sections in text (estimated) | Test | Administrivia |
---|---|---|---|

Week 1: Jan. 21-25 | 1.1-1.5 | No class Monday | |

Week 2: Jan. 28 - Feb. 1 | 2.1-2.5 | ||

Week 3: Feb. 4-8 | 2.7, 3.1, 3.2 | Monday: last day to drop without a "W" or choose the P/F option | |

Week 4: Feb. 11-15 | 3.2-3.4 | ||

Week 5: Feb. 18-22 | 3.4, 3.5 | Midterm #1 | |

Week 6: Feb. 25 - March 1 | 4.1-4.5 | ||

Week 7: March 4-8 | 4.6-4.8 | ||

Week 8: March 11-15 | 4.8-4.9, 5.1-5.4 | ||

Week 9: March 18-22 | Spring break! | ||

Week 10: March 25-29 | 5.5, 5.6 | Midterm #2 | |

Week 11: April 1-5 | 5.7, 6.1, 6.2 | Monday: last day to drop or choose to get a letter grade | |

Week 12: April 8-12 | 6.3-6.5, 6.7 | ||

Week 13: April 15-19 | 7.1-7.4 | ||

Week 14: April 22-26 | 7.7, 7.8 | ||

Week 15: April 29 - May 3 | 8.1-8.4 |

You can think about how you would draw a tree for permutations. If repetitions are allowed, you know how to draw each level. How is the tree affected if repetitions aren't allowed?

- All probabilities are between 0 and 1. If you get something bigger or smaller, there's a mistake somewhere.
- If you're trying to calculate P(E) and the calculation is long and involved, figure out what E^c is and see if calculating P(E^c) would be any simpler. If so, use that and apply Proposition 4.1.

Here's the problem I promised you: If you roll three fair, six-sided dice, it makes sense at first that a sum of 9 and a sum of 10 have equal probability since they can both be obtained in three ways:

9 = 1+2+6, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3

10 = 1+3+6, 1+4+5, 2+4+4, 2+3+5, 2+2+6, 3+3+4

Compute the actual probabilities of these sums and show that a sum of 10 is more likely than a sum of 9. Do you understand why?

We've been using Venn diagrams for about a week now, and I mentioned that I found a diagram with 4 sets very difficult to draw. Someone has made a Venn diagram with 7 sets. Take a look at it, and don't forget to flip it over!

Remember that you use Bayes's Theorem when you have P(E) and P(F|E) and you want to find P(E|F).

The New York Times article I mentioned can be found here.

Example 4c is easily the longest and most challenging example in Section 4.4.

Example 6g is more challenging than the rest of the examples in Section 4.6.

Examples 7b is a good example of a Poisson being used to approximate a binomial, and example 7d is a very challenging one.

Second of all, at this point, we have four basic kinds of discrete random variables. At this point, it might help you to start making a table of types of random variables. With each, you could include (1) the general kind of situation it applies to, (2) a particular situation it applies to, (3) the parameters you need to calculate its p.m.f., (4) the formula you need to calculate its p.m.f., (5) the formula for its expected value, and (6) the formula for its variance. Are there any other factors that might help you learn about these distributions?

We didn't officially cover Section 4.10 -- it's basic facts about cumulative distribution functions, most of which I mentioned briefly in class when I defined c.d.f.s in the first place. Reading it might help you study for the midterm, though! Enjoy your spring break.

I really recommend reading Example 1d in Section 5.1.

Remember that the continuity correction is only used when approximating a binomial random variable with a normal random variable!

I recommend working through a few more cases of the conditional distribution we considered in class today. What's P_(X|Y)(1,1)? P_(Y|X)(1,0)?

If you want a harder discrete conditional distribution problem to work on, here's one: Find the jpdf, marginal density functions, and conditional distributions for X and Y, where X is the number of aces in a standard poker hand and Y is the number of kings in that hand.

We also started talking about moment-generating functions today and worked through finding one for a binomial random variable. Poisson and exponential random variables are naturals for moment-generating functions due to the presence of an e: try calculating those!

I am delighted to say that all the examples in Section 8.3 are quite readable!

Also, the Connecticut state shellfish is the Eastern Oyster.