Study guide of topics covered for Final Exam
ST 371
Devore


Textbook chapters covered: 1 - 5

Material covered before Midterm 1:

Notion of a population;
Notion of a sample;
Definition of a variable;
Definition of a discrete variable;  
Definition of a continuous variable;
Frequency of data values;
Relative frequency of data values;
Density of data values;
Bar plot of discrete data;
Histogram of continuous data;
Choosing the bins for histograms of continuous data;
Describing the shape of a distribution (e.g., mode(s) and skew);
Measures of location;
Notion of a population mean;
Definition of the sample mean;
Notion of a population median;
Definition of the sample median;
Properties of the sample mean and sample median;
Notion of robustness of statistics;
Construction of other quantiles/quartiles/percentiles;
Measures of variability;
Deviations from the mean;
Deviations from the median;
Squared deviations;
Definition of the sample variance;
Definition of the sample standard deviation;
Alternative expressions for the sample variance;
Properties of the sample variance;
Interquartile range (i.e., fourth spread);
Notions of outliers and extreme data values;
Box plots;
Sample space of an experiment;
Notions of outcomes and events;
Relations from set theory (e.g., complement, union, intersection);
Notion of mutually exclusive (or disjoint) events;  
Definition of a probability measure from axioms;
Properties of probability measures (derived from the axioms);
Counting techniques;
Product rules for counting;
Combinations of sets;
Permutations of sets;
Definition of conditional probability;
Multiplication rule for probabilities of intersections;
Law of total probability (and proof);
Bayes' Theorem (and proof);
Notion of independence of two events;
Notion of dependence of two events;
Product rule for independent events;
Necessary and sufficient conditions (and equivalent definitions) for independence;
Notion of mutual independence of a finite collection of events;


Material covered after Midterm 1:

Definition of a random variable;
Distinction between a discrete and continuous random variable;
Probability mass function (pmf) and defining properties;
Parameter of a distribution;
Cumulative distribution function (cdf) and defining properties;
Uses of a pmf and cdf in evaluating probabilities;
Expected value of a discrete random variable;
Variance and standard deviation of a discrete random variable;
Binomial distribution and properties (pmf, cdf, expected values, variance, etc.);
Negative binomial distribution and properties (pmf, cdf, expected values, variance, etc.);
Hypergeometric distribution and properties (pmf, cdf, expected values, variance, etc.);
Poisson distribution and properties (pmf, cdf, expected values, variance, etc.);
Relationship between Poisson and binomial distributions;
Definition of a continuous random variable;
Probability density function (pdf) and defining properties;
Uses of a pdf and cdf in evaluating probabilities;
Expected value of a continuous random variable;
Variance and standard deviation of a continuous random variable;
Uniform distribution and properties (pdf, cdf, expected values, variance, etc.);
Standard uniform distribution;
Gaussian distribution and properties (pdf, cdf, expected values, variance, etc.);
Standard normal distribution;
Standardization of a random variable;
Relationship between Gaussian and binomial distributions;


Material covered after Midterm 2:

Exponential distribution;
Waiting times, inter-arrival times, and relationship between Poisson and exponential distributions;
Definition of the gamma function;
Gamma distribution;
Standard gamma distribution;
Relationship between the gamma and exponential distributions;
Chi-squared distribution;
Relationship between the Chi-squared and gamma distributions;
Weibull distribution;
Relationship between the Weibull and exponential distributions;
Lognormal distribution;
Beta distribution;
Standard beta distribution;
Relationship between the beta and uniform distributions;
Joint pmf and pdf of two random variables;
Marginal pmf and pdf of two random variables;
Independence of two random variables;
Joint pmf and pdf of finitely many random variables;
Marginal pmf and pdf of finitely many random variables;
Independence of finitely many random variables;
Conditional pmf and pdf;
Expected values of real-valued functions of jointly distributed random variables;
Covariance between two random variables, and related properties;
Correlation between two random variables, and related properties;
Relationship between correlation/covariance and independence;
Definition of a statistic;
Definition of a random (iid) sample;
Sampling distribution of a statistic;
Mean and variance of a sample mean;
Distribution of the sample mean of a Gaussian random sample;
Central limit theorem and Gaussian approximations;
Definition of a linear combination of finitely many random variables;
Mean and variance of a linear combination of finitely many random variables;