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 (oldfashioned, not app!)
Contents:
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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
which?)
(when to use
• Variance and standard
deviation (for population or for
sample) ?
• Coefficient of Variation (What
is it for?)
• Percentiles
special cases)
(median, quartiles as
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)