Lecture Notes - Part 2

2/17/04 - Tuesday

Admin Topics Return remaining tests Collect Quiz 2 Quiz 3 due Thursday Quiz 4 due Tuesday 2/24 Read your email! Review web site before each class Be thinking about a project topic Tips Success depends on doing problems Anxiety diminishes with success Success depends on doing problems Anxiety diminishes with success ... Success depends on success! 90% of test questions come from problems! Lecture Topics Chapter 5.1 Samples space, events, experiments Probability distribution Sets: union, intersection, complement, counting, empty set Set notation Games of chance: dice, cards, spinners, colored balls, coin flipping Handout lucky "die" Distribution of one and two dice Sampling with and without replacement Review rules of dice game "Game of 10" Questions for Review What is a probability distribution? What is a set? Anxiety Reducer Math symbols are often used in more than one way just as words can have very different meanings depending upon context. Consider the double bar symbols |x| and |A|.In one case it means the absolute value of x in the other it means the number of elements in the set A. This should be no more confusing than the work "die" meaning to cease to exist and meaning a single "dice" in another case. Don't make it into a bigger deal than it is! And how about that word "tip," tip for money, tip or advice, tip for spill, and so it goes. Life is ambiguous.

2/19/04 - Thursday

Admin Topics Birthday match ups Collect Quiz 4 Questions on Quiz 3 Revised game data sheet Remember Quiz 3 due next Tuesday All tests will be cumulative Last day to drop Feb 20! Tips Lazy is doing unimportant things before important things. Lazy is doing what is easy rather than what is hard. Lazy is not doing all the problems. Lazy is not asking for help Lazy is accepting a "C" when you can get an "A." Life is short - MAXIMIZE IT! Lecture Topics Chapter 5.1 and 5.2 Probability distribution - again and again! Odds for and against Fundamental counting principle Tree diagrams Additive and mulitplicative properties Coin flipping experiments Independent events Questions for Review What is the y-intercept form of a line? What is the x-intercept form of a line? What is a probability distribution? What is the sum of the numbers from 1 to 34? Using set notation for the number of elements in a set, write the equation for the probability of an event A in the sample space S? Anxiety Reducers Become familiar with the manner in which letters and symbols are used in mathematics.Think of them as "math grammar," not fun but necessary. Review the survival guide to formulas and test your knowledge by writing descriptions in words and giving three examples. Remember, writing is always more rigorous than speaking. I still think I can get the entire course condensed into 15 pages.

2/24/04 - Tuesday None of my goals for this day were met! We spent the entire day on the dice game problem. That was not necessarily bad, but it is not what I had planned. We will tackle this material on Thursday. We did introduce the concept of factorial, which will save some time when we do permutations on Tuesday of next week.

Admin Topics Return quizzes Revised due date for Q3, now Thu 2/26 All the questions you had on Q3 should have been asked last Thursday!! That's why I gave two classes to do it. Q5 due Tue 3/2 Using EXCEL Emailing quizzes Mail box in math office Tips When graphing a straight line, you only need two points. Use a third point to check your work, and you are done. To practice graphing, consider the equation cx + dy + e = 0   Look at this! Create 10 practice equations by substituting arbitrary numbers for c, d, and e. Graph them. Don't forget to put some negative numbers in. You must practice, practice, practice. As a short cut, find the y-intercept and x-intercept form of the line in terms of c, d, and e. What are the points (0,b) and (a,0) in terms of c, d, and e? Sounds like a good test question! Remember, when graphing an equation, it is always easier to use two points rather than the slope and a point. Repetition is the key to learning! Build your confidence by doing the problems. There is no way to learn math without doing the problems. Do you think you could learn French without speaking or writing? Of course not. Do the problems and your confidence will sore along with your grade. You learn it by doing it! Lecture Topics Chapter 5.3 - Should have read all of Ch 5 Review Questions Binomial experiments (263, 266,221) Coin flipping experiments E5.2b,E5.3,E5.4,P5.1-5,P5.2-45-48 Pascal's triangle (263) - another mystery of math! Venn Diagrams (8-9, 166, 265) Conditional probabilities 264 Independent events 267 Expected value (269) Random numbers (169)- 10 sided die Odds for and against (245) - One more time Review Questions Given a set of frequency counts, how do you make it a probability distribution? What is the x-intercept form of a line? Derive the y-intercept from the x-intercept equation What is the sum of integers from 1 to 48? What is the multiplicative law of tree diagrams? Anxiety Reducer When answering questions in class, don't be afraid to be wrong. When learning any new subject, you have to expect to be wrong on occasion. Think of it like learning a foreign language; you have to speak it to learn it. Learning math is just like learning a foreign language, because, "guess what!", it is a foreign language. Do you stop speaking and writing English because you make mistakes? No, you continue to practice and keep improving, continuing to learn by doing. It's a life long process. Now, what's the big deal with speaking math and making a few mistakes?

2/26/04 - Thursday Admin Topics Exam 2 on Chapter 5 is Mar 4 Quiz 4 Dice Game due today Quiz 5 due on Tuesday Mar 2 You can turn in homework four ways In class - preferred In box in math office Email - prof@focusware.com Fax - 703-266-9344 If you can, use EXCEL for homework Tips Odds always concern a binomial event: something happening versus something not happening, usually a win or lose situation. Odds are usually used for one-time events, which will not be repeated again, at least not under exactly the same conditions. The most common examples are horse races and sporting events. Odds are based on the past performance of a horse or team against similar competitors. Odds are much more difficult to calculate because there is no specific historical information for the exact event about to take place. The best you can do is look at past performance under similar situations. You can think of odds as the number of times team A would win (n) compared to the number of times team B would win (m), if they played each other n+m times. What are the odds you will do well on your test? Past perfromance predicts future performance! Lecture Topics Chapter - READ IT! READ IT! READ IT! Review Questions Binomial experiments (263, 266,221) Coin flipping experiments E5.2b,E5.3,E5.4,P5.1-5,P5.2-45-48 Pascal's triangle (263) - May not get there until after break Venn Diagrams (8-9, 166, 265) Conditional probabilities 264 Independent events 267 Expected value (269) Random numbers (169)- 10 sided die Odds for and against (245) - Read this. There is no time to discuss before the test. Questions for Review What is a binomial event? How do you convert frequency counts into a probability distribution? What is an independent event? Anxiety Reducer Read the material ahead of time and your learning experience will explode. The maximum learning takes place when you know 30-50% of the material going into a lecture. If all of the material is totally new, it is very difficult to follow the lecture.

3/2/04 - Tuesday

Admin Topics Revised Test Date Tips A probability distribution is a set of numbers between 0 and 1, all of which add up to one. A random variable is a variable which takes on values according to a probability distribution. It varies but within the restrictions of its probability distribution. A tree diagram is the best way to visualize the alternatives in the dice game. The purspose of the dice game was to get you to understand that, even though results are determined by chance, there is aften a best strategy given the probabilities. . There will be variations due to the randomness of the events; however, in the long run, there is a best strategy which you should follow. If you played a 1000 games, you would have a hard time telling the difference between the theoretical distribution and the experimental one. Once you have developed rules for the best strategy based upon probabilities, there is no longer any guess work. You MUST follow the rules to get the best result. There is no such thing as taking an uncalculated risk. You have done the calculations and now know what the optimal strategy is. Many decisons in life can be reduced to probabilities to incease your chances of success. Lecture Topics Counting Formulas Fundamental Counting Principle n events, k experiments n factorial Permutations Combinations Questions for Review Formula for expected value Formula for conditional probability Formula for prob of (A union B) Anxiety Reducer Review in detail the answers to all problems that are posted on the web?

3/4/04 - Thursday

Admin Topics Chapter 5 Test March 18 Tips Expected values are really just another version of weighted averages. Take a look at the following general form for a weighted average: If each one of the weights is thought of as frequency of x, then Now, if we divide each of the frequencies by the sum of the frequencies, we get a probability: which takes us full circle and gives us the formula for expected values in terms of probabilities: Lecture Topics Dice Game Probability Tree Quiz 5 probability problem Expected value of prob problem Weighted averages p.189 Problem 19, p.191 Grade point averages Binomial probability distribution Lottery problem p.282 Questions for Review Formula for expected value Formula for conditional probability Formula for prob of (A union B) Anxiety Reducer The factorial sign (exclamation point) is just another piece of shorthand notation like the summation sign. It is just a lot easier to write 5! rather than 5x4x3x2x1. Remember that n! = n(n-1)! = n(n-1)(n-2)! and so on. Don't let it intimidate you. It is just another new math verb.

3/16/04 - Tuesday

Admin Topics Test on Chapter Five Project Proposals March 18, 2004 Lecture Topics Review Test Topics Binomial probability distribution