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Date: 25 Jan 2005, 09:36:09 AM Subject: 315 Exam coverage Week 3 slide 24, the first row of the table, the last entry should be 0.8405. I've posted a .pdf version of Week 2 key on the website (some are unable to read the .doc version). FROM MY PREVIOUS MESSAGE: For week 3 (begins Monday, January 24) you are to read pp. 94-96 lightly but will not be tested on it. Read pp 97-136 carefully, especially concentrating on Bayes Formula, tree diagrams and the OIL example (to be introduced in the in the lecture slides not yet posted). Carefully study expected value of random variable, variance and standard deviation of random variable, properties E (a X + b Y + c) = a E X + b E Y + c and s.d (a X + b) = |a| s.d.(X), where a b c are constants and X, Y are random variables. Also, for INDEPENDENT random variables E (XY) = (E X) (E Y) and Var(X + Y) = Var(X) + Var(Y). FROM MY PREVIOUS MESSAGE: Our next readings are in Probability. Lectures will not meet Monday. Carefully read pp 70-93 for Wednesday lecture. I will post the slides tomorrow (Friday) afternoon and suggest exercises at that time. This is an interesting part of 315 and my experience is that students gain a solid understanding of probability from this course. Your main focus: 1. The set of all possible outcomes and its subsets "the events" as a model for probability. Union, intersection, complements of events. Venn's diagram. 2. Addition rule for probabilities, e.g. P(rain today or tomorrow) = P(rain today) + P(rain tomorrow) - P(rain both days). 3. Multiplication rule for probabilities, e.g. P(rain today and tomorrow) = P(rain today) times the conditional probability of rain tomorrow given that it has rained today, written P(rain both days) = P(rain today) P(rain tomorrow | rain today). The previous expression has in it a vertical bar (not a division sign) with the event whose probability is sought left of the bar and the conditioning event right of the bar. So if we think there is a 40% chance of rain today and if we think there is a 3% chance of rain tomorrow if it does indeed rain today then P(rain both days) = 0.4 times 0.03. 4. Independence of events means having one event occur does not affect the probability of the other. If P(rain tomorrow) is not affected by whether it rains today that would be an example (if it were true). In such a case P(rain tomorrow | rain today) = P(rain tomorrow). 5. We'll use the example of drawing colored balls from a box e.g. if drawing with replacment from {R R R B B} then P(R1) = 3/5 (red on draw one). Because we replace balls P(R1 and R2) = P(R1) P(R2 | R1) = (3/5) (3/5). We've used the fact that if a red is drawn on draw one the conditional probability of a red on draw two remains 3/5 (we've replaced the red). On the other hand, if we do not replace balls P(R1 and R2) = (3/5) (2/4) since the second draw is from 4 balls, only two of which are red if a red was slected first. FROM MY PREVIOUS MESSAGE: For the syllabus and other materials pertaining to Statistics 315 go to www.stt.msu.edu/~rdl Once there, clicking on STT 315 takes you to the materials. Clicking on any offering, such as the syllabus, will result in that file being downloaded. The syllabus is small but the powerpoint slides may run to a couple of megabytes. If you work over a modem keep this in mind. For now, look over the syllabus and the slides found on the website. When you print the slides it is best to print them 6 to each page. Kindly do not reply to this message but do bring up your questions in class. STT 315 students should be "gently" reading all of chapter 1 of the textbook, but pay careful attention to matters concerning the sample and population standard deviations. I will focus on skills pertaining to the readings but narrow them (or in some cases enlarge upon them) vis-a-vis the powerpoint slides found on the website. These matters include: use of table 14 (random numbers) to conduct random sampling with-replacement vs without-replacement sampling why sample at random? calculation of sample standard deviation s from the definition calculation of s by "short cut" method (more subject to rounding errors) what happens to s if all numbers on a list are multiplied by a constant? what happens to s if a constant is added to all numbers on a list? margin of error: (estimate) +/- (estimated standard error of the estimate) special case of above: (sample mean) +/- (s / root(n) ) (n is sample size) Great Trick of Statistics histogram vs density picture of data; the issue of resolution how to make a density from a list of numbers (do by eye for a few values) with replacement is about the same as without if root( (N-n) / (N-1) ) is near 1 NOTE CORRECTION cloning a population how many with-replacement samples vs without? THE FOLLOWING INFORMATION IS NEW. YOUR PREPARATION FOR EXAM 1, WEDNESDAY FEBRUARY 2: Look over the slides for Weeks 1, 2, 3, and prepare to solve questions of the type discussed there. Likewise, consult the recitation assignments and prepare to solve questions of like kind. Consult your textbook as needed per the readings announced in my earlier emails reported above. On next Monday I will be able to answer questions concerning any of this material. The exam itself will be hand written and you will then select a multiple choice response to match your answer and record that on a scan sheet. BOTH THE SCAN SHEET AND YOUR HAND WRITTEN EXAM PAPER WITH YOUR SIGNATURE WILL BE REQUIRED. IF ONE IS NOT SUBMITTED YOU WILL EARN 0.0. Arrive early enough to assist us with seating. You will be assigned seating for this exam. ANY STUDENT WHO BEGINS THE EXAM IN A SEAT OTHER THAN THE ONE ASSIGNED TO THEM MAY BE ASKED TO LEAVE AND WILL EARN 0.0 AT THE DISCRETION OF THE INSTRUCTOR. You can expect 20 questions. Points may be withdrawn for answers given without justification. You must show enough work to enable us to see that you know what you are doing. Some students will be audited and their scantron score may be altered to reflect the work they have shown on the written exam. If you are prepared as outlined above this exam should pose no unexpected difficulties. The textbook exercises are keyed to sections of the book which will also give you an idea of where the emphasis lies. R