\(\newcommand{\reals}{\mathbb{R}} \newcommand{\expect}{\mathbb{E}} \newcommand{\var}{\mathbb{V}} \newcommand{\corr}{\mathrm{corr}} \)

Information about Midterm 3 (now updated for Fall 2012)

NOTE: Last updated at 3:05pm on November 15, 2012.

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General Information

Specific information

This is a discussion of various topics related to the material of the course and it is meant to complement the practice test in various ways. It is not meant to be a precise list of topics covered by the test.

Sample spaces

Random variables

Conditional probability

A note on notation

I will use the notation \[ \expect{X} = \mu_X \] for the expected value (mean) of a random variable \(X\). Note that in some browsers the bar in \(\bar{X}\) will not show if \(\bar{X}\) is in the subscript. If you don't see a bar below, you should watch out for this problem: \[ \expect{\bar{x}} = \mu_{\bar{x}} \] Similarly, we will use two notations as synonymous \[ \var{X} = \sigma^2_{X} \] for the variance of the random variable \(X\).

List of Chapter 5 topics covered

The binomial distribution (Section 5.1)

Proportions \(\hat{p}\)

Chapter 6 and Chapter 7

The main difference between Chapter 6 and Chapter 7 is that in Chapter 6 the standard deviation is given (somewhat misteriously, it is known), while in Chapter 7 we estimate it using the sample variance. This results in the change of the normal distribution as sampling statistic of the z-score for \(\bar{x}\) \[ z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} \] to the t-statistic \[ t = \frac{\bar{x}-\mu}{SEM} \] where \[ SEM = \frac{s}{\sqrt{n}}.\] is the standard error of the mean and is a statistic.

Sampling distribution

Confidence intervals

Hypothesis testing

The Student t-distribution

The list of Chapter 8 topics covered

NOTE: Information in this section will be useful for the next homework, and the Final Exam, but not for Midterm 3.

Inference for single proportion

Inference for 2 proportions