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

Week 1: Jan. 17-20 | 2.1, 1.1 | ||

Week 2: Jan. 23-27 | 1.1, 1.3, 1.4 | ||

Week 3: Jan. 30 - Feb. 3 | 1.4, 1.5, 1.6 | Monday: last day to drop without a "W" or choose the P/F option | |

Week 4: Feb. 6-10 | 2.2, 2.3 | ||

Week 5: Feb. 13-17 | 2.4 | Midterm #1 | |

Week 6: Feb. 20-24 | 3.1, 3.2, 3.3 | ||

Week 7: Feb. 27 - March 2 | 3.4, 5.1 | ||

Week 8: March 5-9 | 5.1, 5.2, 5.3 | ||

Week 9: March 12-16 | Spring break! | ||

Week 10: March 19-23 | 5.4 | Midterm #2 | |

Week 11: March 26-30 | 5.5, 6.1 | Monday: last day to drop or choose to get a letter grade | |

Week 12: April 2-6 | 6.2, 6.3 | ||

Week 13: April 9-13 | 6.4, 6.5 | ||

Week 14: April 16-20 | 6.6 and moment-generating functions | ||

Week 15: April 23-27 | moment-generating functions and review |

You might also want to think about why the formula for C_(n,k) is true. Let me summarize what I said in class again:

Suppose you want to choose 3 out of the 7 movies you own to watch over a weekend. You could start by pulling 3 of them out of a bag and setting them down in a row. There are P_(7,3) ways to do that. Suppose that what you ended up with was the following order:

- E.T.
- Ghostbusters
- Das Boot

- Often, it's easier to count the number of ways to get the kind of thing you don't want than the kind of thing you do. Instead of counting all the things you want, you can find the total number of possibilities and subtract out the ones you don't. For instance, if I want to know all the ways to roll two different-colored standard six-sided dice and get a sum greater than 3, I can count like this: There are 36 possible rolls. Of these, 3 give sums less than or equal to 3: 1-1, 1-2, and 2-1. Therefore, there are 36-3=33 ways to roll these dice and get a sum bigger than 3.
- If you've calculated the number of poker hands (for instance) and you want to check your calculation, think about whether you're overcounting. Are there two different ways to get the same hand using the method you used? If so, then you need to think of a new way to get the answer.

I've been asked if I could recommend another book as a supplement. Some of my colleagues suggest __A First Course in Probability__ by Sheldon Ross (it used to be used for this course at UConn). I would personally suggest __Introduction to Probability__ by Charles M. Grinstead and J. Laurie Snell. You can get it free online here. If you use either, please let me know how helpful it is to you so I can make better recommendations for future classes (and if you find another useful source, please let me know about it, too).

We talked in class today about the limitations of only knowing a random variable's expected value and not its variance. What kind of information do you get if you know a random variable's variance but not its expected value, and what would you *not* know?

- the general situation it models,
- the possible outcomes (for a geometric distribution, that's {1,2,3,4,...}; for binomial(n,p), that's {0,1,2,...,n}),
- the formula (if there is one),
- formulas for the expected value and variance, and
- a fully worked out example.

Remember the rule of thumb I gave you in class today: At this point, if there is nothing that clearly triggers the event happening (like flipping a coin, rolling a die, drawing a poker hand, or gathering people in a room), the Poisson distribution is probably the best model we have.

Just play around with them. They're meant to go with a different textbook, but they're still fun and useful. Let me know if there's something you find in them that you'd like to talk about!

Craps: Here are Frank Sinatra and Dean Martin and Marlon Brando (believe it or not) singing a couple songs from "Guys and Dolls."

Bayesian probabilities: There's a very nice discussion of conditional probabilities in this New York Times article. Take a look at the notes at the end, too!

You are a general being advised by two of your lieutenants. One of them tells you that in general, the probability of an attack on your left flank is 1/5, the probability of an attack on your right flank is 3/10, and the probability of a frontal attack is 1/2. The other one has been keeping track of the enemy's communication channels and tells you that if they're going to attack on the left, the probability of this chatter is 1/5, if they're going to attack on the right, the probability of this chatter is 7/10, and if they're going to attack frontally, the probability of this chatter is 1/10. Given that you are, in fact, hearing this chatter, can you work up a probability profile for the attack?

- an expected value and a variance,
- an expected value but no variance, and
- neither an expected value nor a variance.

I also left you with a puzzle at the end of class: find a discrete distribution with no median. Enjoy your break!