{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Section 1.3

# Section 1.3 - Contents I Probability 5 1 Sets and...

This preview shows pages 1–9. Sign up to view the full content.

Contents I Probability 5 1 Sets and Probability 7 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . 12 1.1.3 Proportions . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . 32 1.3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1.3.1 Random Experiments, Sample Spaces and Events . . . 57 1.3.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . 63 1.4 Conditional Proportions and Probabilities . . . . . . . . . . . 81 1.4.1 Conditional Proportions . . . . . . . . . . . . . . . . . 81 1.4.2 Conditional Probabilities . . . . . . . . . . . . . . . . 84 1.4.3 Multiplicative Rule . . . . . . . . . . . . . . . . . . . . 87 1.4.4 Independence . . . . . . . . . . . . . . . . . . . . . . . 88 1.5 Compound Experiments . . . . . . . . . . . . . . . . . . . . . 100 1.5.1 Finding Probabilities and Conditional Probabilities in Compound Experiments . . . . . . . . . . . . . . . . . 101 1.5.2 Notation for Events in Compound Experiments . . . . 110 1.5.3 Using the Multiplicative Rule to Find Probabilities in Compound Experiments . . . . . . . . . . . . . . . . . 112 1.5.4 More Examples . . . . . . . . . . . . . . . . . . . . . . 117 1.6 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 137 2 Variables 153 2.1 Variables and their Distributions . . . . . . . . . . . . . . . . 154 2.1.1 Basic Definitions of Variables and Random Variables . 154 2.1.2 Classifying Variables . . . . . . . . . . . . . . . . . . . 157 2.1.3 Distributions of Variables and Random Variables . . . 158 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 CONTENTS 2.1.4 Distributions of Categorical Variables . . . . . . . . . 160 2.1.5 Distributions of Numerical Discrete Variables . . . . . 165 2.1.6 Distributions of Numerical Continuous Variables . . . 170 2.2 Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 2.3 Mean and Standard Deviation . . . . . . . . . . . . . . . . . . 201 2.3.1 The Mean . . . . . . . . . . . . . . . . . . . . . . . . . 201 2.3.2 Variance and Standard Deviation . . . . . . . . . . . . 210 2.4 Joint Distributions . . . . . . . . . . . . . . . . . . . . . . . . 225 2.5 Association Between Variables . . . . . . . . . . . . . . . . . 242 2.5.1 Conditional Distributions . . . . . . . . . . . . . . . . 242 2.5.2 Independence . . . . . . . . . . . . . . . . . . . . . . . 246 2.5.3 Observing Association in Scatterplots . . . . . . . . . 249 2.5.4 Covariance . . . . . . . . . . . . . . . . . . . . . . . . 253 2.5.5 Correlation . . . . . . . . . . . . . . . . . . . . . . . . 257 2.5.6 Properties of Correlation . . . . . . . . . . . . . . . . 263 2.6 Combining Variables . . . . . . . . . . . . . . . . . . . . . . . 277 2.6.1 Y = f ( X ) . . . . . . . . . . . . . . . . . . . . . . . . . 277 2.6.2 Y = aX + b . . . . . . . . . . . . . . . . . . . . . . . . 279 2.6.3 W = f ( X, Y ) . . . . . . . . . . . . . . . . . . . . . . . 283 2.6.4 W = aX + bY + c . . . . . . . . . . . . . . . . . . . . 284 2.6.5 Portfolio Analysis . . . . . . . . . . . . . . . . . . . . 291 2.6.6 Sums of Many Variables . . . . . . . . . . . . . . . . . 294 3 Important Families of Distributions 303 3.1 Using Distributions to Find Probabilities . . . . . . . . . . . 304 3.2 Binomial and Hypergeometric Distributions . . . . . . . . . . 307 3.2.1 The Binomial Distribution . . . . . . . . . . . . . . . . 307 3.2.2 The Hypergeometric Distribution . . . . . . . . . . . . 315 3.2.3 The Binomial Distribution as an Approximation to the Hypergeometric Distribution . . . . . . . . . . . . 322 3.3 The Poisson and Exponential Distributions . . . . . . . . . . 331 3.3.1 Poisson Processes . . . . . . . . . . . . . . . . . . . . . 331 3.3.2 Poisson Distributions . . . . . . . . . . . . . . . . . . . 332 3.3.3 Exponential Distributions . . . . . . . . . . . . . . . . 338 3.4 The Uniform and Normal Distributions . . . . . . . . . . . . 348 3.4.1 Uniform Distributions . . . . . . . . . . . . . . . . . . 348 3.4.2 Normal Distributions . . . . . . . . . . . . . . . . . . . 351 3.5 Sampling Distributions . . . . . . . . . . . . . . . . . . . . . . 373 3.5.1 Mean and Standard Deviation of Σ X and ¯ X . . . . . 375 3.5.2 Complete Distribution of Σ X and ¯ X . . . . . . . . . . 377
CONTENTS 3 3.5.3 The Normal Approximation to the Binomial Distribu- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 3.5.4 Normal Approximation to the Poisson Distribution . . 391 II Statistics 397 4 Estimation 399 4.1 Point Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 400 4.1.1 Parameters, Statistics and Point Estimators . . . . . . 400 4.1.2 Assessing the Quality of a Point Estimator . . . . . . 402 4.1.3 Point Estimators for Common Parameters . . . . . . . 406 4.2 Introduction to Interval Estimation . . . . . . . . . . . . . . . 415 4.2.1 Guiding Example and Definition . . . . . . . . . . . . 415 4.2.2 Confidence Interval for μ when σ is Known . . . . . . 420 4.2.3 Determining the Sample Size . . . . . . . . . . . . . . 423 4.2.4 A Closer Look at Confidence Intervals . . . . . . . . . 424 4.3 More Confidence Intervals . . . . . . . . . . . . . . . . . . . . 428 4.3.1 Estimating μ when σ is not known . . . . . . . . . . . . 428 4.3.2 Estimating a population proportion, p . . . . . . . . . . 436 5 Hypothesis Testing 445

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 CONTENTS
Part I Probability 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 1 Sets and Probability 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1.3. PROBABILITY 57 1.3 Probability 1.3.1 Random Experiments, Sample Spaces and Events A random experiment is an activity that has more than one possible out- come and whose outcome is unpredictable. The set of all possible outcomes
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 40

Section 1.3 - Contents I Probability 5 1 Sets and...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online