Math 4030 Midterm Exam Review

General Info: Wed. Oct. 26, Lecture Hours & Rooms Duration: 80 min. Close-book 1 page formula sheet (both sides can be used), that will be handed in with the exam paper. No examples on the sheet. Non-programmable Calculator (old- fashioned, not app!)

Contents: Basic Concepts Descriptive statistics Sample space and events Classical probability and counting rules Random variables Discrete distributions Continuous distributions

Basic concepts: Population vs sample Variable vs Data (values) Types of variables Levels of measurement Mutual exclusive events Independent events Random variables: discrete vs. continuous

Descriptive statistics Tables: frequency tables (Grouped or ungrouped? How to define classes?) Graphs: bar chart, histograms, Pareto chart, Pie chart, Dot diagram, Box-plot and outliers, and stem-and-leaf (Which chart would you recommend?)

Descriptive statistics Mean and median (when to use which?) Variance and standard deviation (for population or for sample) ? Coefficient of Variation (What is it for?) Percentiles (median, quartiles as special cases)

Sample Space and Events: List all outcomes in a sample space; List all outcomes in an event; Use Venn’s diagram to identify compound events (Union, intersection, and complement)

Count: How many ways to … Multiplication; Permutation; Combination; Factorial Tree diagram can be helpful.

Classical Probability: Identify sample space; Identify event; Check if classical probability applies; Count …

Probability Rules: Addition rule: mutually exclusive Product rule: independent Conditional probability (Bayes’ Theorem) Complement rule Venn diagram and tree diagram may help

Random Variables: Define a random variable; Distribution of a discrete random variable; Discrete: Probability function f(x) vs. Cumulative distribution function F(x) Continuous: pdf vs CDF Mean and variance Chebyshev’s Theorem

Discrete distributions: Binomial: parameters, formula for probabilities Poisson: parameter, formula for probabilities Hypergeometric: parameters, formula, (sampling with replacement vs. without replacement) Geometric: parameter, formula. Let X be …, then X follows …

Continuous distributions: Uniform: parameters/interval, constant, probability can be found geometrically. Normal: –Standard normal and Table 3 (Table 3 will be provided.) –Conversion between standard normal and general normal. –Find probability using Table 3. –Find cut-off values using Table 3. –z  notation –Normal approximation to binomial (correction for continuity)