Probability and statistics

159 Pages·2001·1.834 MB·English

by  Srinivasan, R. Alu;Schiller, John J.;Spiegel, Murray R.;LeVan, Mike

Easy
SCHAUM’S OUTLINES
P
ROBABILITY
S
AND TATISTICS
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Easy
SCHAUM’S OUTLINES
P
ROBABILITY
A S
ND TATISTICS
BASED ON SCHAUM’S Outline of
Probability and Statistics
BY MURRAY R. SPIEGEL, JOHN SCHILLER,
AND R. ALU SRINIVASAN
ABRIDGMENT EDITOR
M L V
IKE E AN
SCHAUM’S OUTLINE SERIES
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DOI: 10.1036/0071398384
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Contents
Chapter 1 Basic Probability 1
Chapter 2 Descriptive Statistics 14
Chapter 3 Discrete Random Variables 23
Chapter 4 Continuous Random Variables 34
Chapter 5 Examples of Random Variables 42
Chapter 6 Sampling Theory 58
Chapter 7 Estimation Theory 75
Chapter 8 Test of Hypothesis and
Significance 85
Chapter 9 Curve Fitting, Regression,
and Correlation 99
Chapter 10 Other Probability Distributions 117
Appendix A Mathematical Topics 132
Appendix B Areas under the Standard
Normal Curve from 0 to z 136
Appendix C Student’s t distribution 138
Appendix D Chi-Square Distribution 140
Appendix E 95th and 99th Percentile Values
for the F Distribution 142
Appendix F Values of e−λ 146
Appendix G Random Numbers 148
Index 149
v
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Chapter 1
B
ASIC
P
ROBABILITY
IN THIS CHAPTER:
✔
Random Experiments
✔
Sample Spaces
✔
Events
✔
The Concept of Probability
✔
The Axioms of Probability
✔
Some Important Theorems
on Probability
✔
Assignment of Probabilities
✔
Conditional Probability
✔
Theorem on Conditional Probability
✔
Independent Events
✔
Bayes’ Theorem or Rule
✔
Combinatorial Analysis
✔
Fundamental Principle of Counting
✔
Permutations
✔
Combinations
1
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2 PROBABILITYAND STATISTICS
✔
Binomial Coefficients
✔
Stirling’s Approximation to n!
Random Experiments
We are all familiar with the importance of experi-
ments in science and engineering. Experimentation
is useful to us because we can assume that if we
perform certain experiments under very nearly
identical conditions, we will arrive at results that
are essentially the same. In these circumstances,
we are able to control the value of the variables
that affect the outcome of the experiment.
However, in some experiments, we are not able to ascertain or con-
trol the value of certain variables so that the results will vary from one
performance of the experiment to the next, even though most of the con-
ditions are the same. These experiments are described as random. Here
is an example:
Example 1.1. If we toss a die, the result of the experiment is that it
will come up with one of the numbers in the set {1, 2, 3, 4, 5, 6}.
Sample Spaces
Aset Sthat consists of all possible outcomes of a random experiment is
called a sample space, and each outcome is called a sample point. Often
there will be more than one sample space that can describe outcomes of
an experiment, but there is usually only one that will provide the most
information.
Example 1.2. If we toss a die, then one sample space is given by
{1, 2, 3, 4, 5, 6} while another is {even, odd}. It is clear, however, that
the latter would not be adequate to determine, for example, whether an
outcome is divisible by 3.
If is often useful to portray a sample space graphically. In such cases,
it is desirable to use numbers in place of letters whenever possible.