Preparation for Midterm 3 Midterm 3 will be on Chapters 5 and 6 in Devore, and also on the handouts (CLT, LLN, Normal Distributions) from the course website. For Midterm 3: there will be no notes, no calculators, no books allowed. I think it is still managable. For the final you will be allowed to bring a page of notes. Be ready to compute simple arithmetic. Get a good night's sleep. Homework will be rewarded. Ch. 5 Everything in 5.1, and also the Proposition in 5.2 on computing expected value, is fundamental. Devore has done a good job of putting boxes around the summary items you should understand. In particular: you should be able to compute an expected value of a function h(x,y) of two random variables, and you should be able to compute the probability of an event defined in terms of two random variables. Especially note that the joint density function of INDEPENDENT random variables is the product of their individual density functions. Be prepared to compute double integrals. For uniform distribution on a region, probability is proportional to area, and this sometimes simplifies probability computations. For ANY random variables: the expectation of the sum is the sum of the expectations. For INDEPENDENT random variables, we also have: the variance of the sum is the sum of the variances. For example, if X,Y are independent, then E(XY) = E(X)E(Y) and V(X + Y) = V(X) + V(Y) . Note these statements are usually not true without the independence assumption. Consider for example the case Y = -X. Also note you can use the equation for V(X+Y) to find the standard deviation of X+Y (take square root of V). The idea of a sampling distribution of a statistic, described in 5.3, is fundamental to understanding statistics (though somewhat difficult to test on an exam). A statistic is some quantity calculated from sample data. The key idea is that the statistic can be considered as a random variable itself, with its own probability distribution. The most important statistic to understand is the average, Xbar_n (this is (1/n)(X_1 + ... X_n), where _ denotes subscript). We generally consider the case that the X_i are i.i.d. (so they can be thought of as representing a random sample from a population with an underlying probability distribution). Know all about the average as discussed on the CLT and LLN handouts. Also: know the statements of CLT and LLN: not only verbatim, but also the meaning of the assumptions and conclusions. Regarding correlation and covariance: it is sufficient to know the boxed items in 5.2 A linear combination of independent normal random variables is still normal. Understand how to compute the mean, standard deviation and variance of a linear combination of independent random variables. If X is normally distributed, understand how to compute probabilities involving X from the table for the standard normal distribution. Ch. 6 Understand what an estimator is. Know what it means for an estimator to be biased, or consistent. (See the web page item on this.) Know how to compute the MOM and MLE estimators. Specifics - You will have a problem involving computations appealing to the CLT. - You will have a problem requiring computation of an MOM estimator or a problem requring computation of an MLE estimator. Note, there is a MOM handout on the web now. - You will have at least one problem extremely close to a homework problem.