This book is organized into five major parts that explore the main topic areas
in probability. I also include a part that offers a couple quick top-ten references
for you to use. Each part contains chapters that break down each major
objective into understandable pieces.
Part I: The Certainty of Uncertainty:
Probability Basics
This part gives you the fundamentals of probability, along with strageties for
setting up and solving the most common probability problems in the introductory
course. It starts by introducing probability as a topic that has an impact
on all of us every day and underscores the point that probability often goes
against our intuition. You discover the basic definitions, terms, notation, and
rules for probability, and you get answers to those all-important (and often
frustrating) questions that perplex students of probability, such as, “What’s
the real difference between independent and mutually exclusive events?”
You also see different methods for organizing the information given to you,
including Venn diagrams, tree diagrams, and tables. Finally, you discover
good strategies for solving more complex probability problems involving the
Law of Total Probability and Bayes’ Theorem.
in probability. I also include a part that offers a couple quick top-ten references
for you to use. Each part contains chapters that break down each major
objective into understandable pieces.
Part I: The Certainty of Uncertainty:
Probability Basics
This part gives you the fundamentals of probability, along with strageties for
setting up and solving the most common probability problems in the introductory
course. It starts by introducing probability as a topic that has an impact
on all of us every day and underscores the point that probability often goes
against our intuition. You discover the basic definitions, terms, notation, and
rules for probability, and you get answers to those all-important (and often
frustrating) questions that perplex students of probability, such as, “What’s
the real difference between independent and mutually exclusive events?”
You also see different methods for organizing the information given to you,
including Venn diagrams, tree diagrams, and tables. Finally, you discover
good strategies for solving more complex probability problems involving the
Law of Total Probability and Bayes’ Theorem.
Part II: Counting on Probability
and Betting to Win
In this part, you get down to the nitty gritty of probability, solving problems that
involve two-way tables, permutations and combinations, and games of chance.
The bottom line in this part? Probability and intuition don’t always mix!
Part III: From A to Binomial:
Basic Probability Models
In this part, you build an important foundation for creating, using, and evaluating
probability models. You discover all the ins and outs of a probability
distribution; the basic concepts and rules for defining probability distributions;
and how to find probabilities, means, and variances. You work with the
binomial and normal distributions, and you find out how probability ties in to
the major results from statistics: the Central Limit Theorem, hypothesis testing,
and overall decision making in the real world.
Part IV: Taking It Up a Notch:
Advanced Probability Models
In this part, you work with more intermediate probability models that count
and try to predict the number of arrivals, successes, or the number of trials
needed to achieve a certain goal. The probability distributions I focus on are
the Poisson, negative binomial, geometric, and hypergeometric. You find out
how many customers you expect to come into a bank (Poisson distribution);
the number of poker hands you need to draw before you get four of a kind
(geometric distribution); the number of frames you need to bowl before getting
your third strike (the negative binomial distribution); and the probability
of getting a hand in poker (hypergeometric distribution).
Part V: For the Hotshots: Continuous
Probability Models
In this part, you look at some of the models you find in probability and statistics
courses that have calculus as a prerequisite — mainly the uniform
(continuous case) distribution, exponential distribution, and other user defined
probability density functions. You see how to find probabilities and
the expected value, variance, and standard deviation of continuous probability
models. And you apply the models to situations such as the time between arrivals of customers at the bank, time to complete a task, or the length of a
phone call. Note: Calculus is useful but not required for this part. I introduce
the methods that use calculus, but I also provide formulas and other methods
of solution that don’t use calculus for the uniform and exponential.
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and Betting to Win
In this part, you get down to the nitty gritty of probability, solving problems that
involve two-way tables, permutations and combinations, and games of chance.
The bottom line in this part? Probability and intuition don’t always mix!
Part III: From A to Binomial:
Basic Probability Models
In this part, you build an important foundation for creating, using, and evaluating
probability models. You discover all the ins and outs of a probability
distribution; the basic concepts and rules for defining probability distributions;
and how to find probabilities, means, and variances. You work with the
binomial and normal distributions, and you find out how probability ties in to
the major results from statistics: the Central Limit Theorem, hypothesis testing,
and overall decision making in the real world.
Part IV: Taking It Up a Notch:
Advanced Probability Models
In this part, you work with more intermediate probability models that count
and try to predict the number of arrivals, successes, or the number of trials
needed to achieve a certain goal. The probability distributions I focus on are
the Poisson, negative binomial, geometric, and hypergeometric. You find out
how many customers you expect to come into a bank (Poisson distribution);
the number of poker hands you need to draw before you get four of a kind
(geometric distribution); the number of frames you need to bowl before getting
your third strike (the negative binomial distribution); and the probability
of getting a hand in poker (hypergeometric distribution).
Part V: For the Hotshots: Continuous
Probability Models
In this part, you look at some of the models you find in probability and statistics
courses that have calculus as a prerequisite — mainly the uniform
(continuous case) distribution, exponential distribution, and other user defined
probability density functions. You see how to find probabilities and
the expected value, variance, and standard deviation of continuous probability
models. And you apply the models to situations such as the time between arrivals of customers at the bank, time to complete a task, or the length of a
phone call. Note: Calculus is useful but not required for this part. I introduce
the methods that use calculus, but I also provide formulas and other methods
of solution that don’t use calculus for the uniform and exponential.
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