Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Sets
- 3 Probability
- 4 Visualising and quantifying the properties of data
- 5 Useful distributions
- 6 Uncertainty and errors
- 7 Confidence intervals
- 8 Hypothesis testing
- 9 Fitting
- 10 Multivariate analysis
- Appendix A Glossary
- Appendix B Probability density functions
- Appendix C Numerical integration methods
- Appendix D Solutions
- Appendix E Reference tables
- References
- Index
Appendix D - Solutions
Published online by Cambridge University Press: 05 July 2013
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Sets
- 3 Probability
- 4 Visualising and quantifying the properties of data
- 5 Useful distributions
- 6 Uncertainty and errors
- 7 Confidence intervals
- 8 Hypothesis testing
- 9 Fitting
- 10 Multivariate analysis
- Appendix A Glossary
- Appendix B Probability density functions
- Appendix C Numerical integration methods
- Appendix D Solutions
- Appendix E Reference tables
- References
- Index
Summary
2. Sets
2.1 (i) A ∪ B = {1, 2, 3, 4, 5, 9}; (ii) A ∩ B = {1, 3}; (iii) A \ B = {2, 4};(iv) B \ A = {5, 9};(v) Ā = {5, 9}, and B = {2, 4}
2.2 (i) A ∪ B = {0, 1, 2, 3, 5, 6, 9};(ii) A ∩ B = {5}; (iii) A \ B = {0, 2, 6};(iv) B \ A = {1, 3, 9}
2.3 (i) For example see the top part of Figure 2.3; (ii) see Figure 2.2, where A and B are interchanged.
2.4 A ∪ B = R
2.5 A ∪ B = R
2.6 A ∩ B = 1, 2, 3, 4, 5
2.7 A ∩ B = ø
2.8 A ∪ B ∩ C = Z+
2.9 A ∪ B ∩ C = {0, Z-}
2.10 ΩDecimal = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
2.11 {red, green, blue}
2.12 C
2.13 Z
2.14 {x|5 < x < 10}
2.15 {x |x ∈ R}
3. Probability
3.1 4/52 = 0.077 to 3 s.f.
3.2 0.45%
3.3 20/52 = 0.385 to 3 s.f.
3.4 The probability of the getting an ace followed by a 10 point card, where the other player also gets a 10 point card is 0.72%. The probability of getting an ace followed by a 10 point card, where the other player gets a card with a different value is 1.69%. The total probability of being dealt an ace followed by a 10 point card is the sum: 2.41%.
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- Statistical Data Analysis for the Physical Sciences , pp. 201 - 206Publisher: Cambridge University PressPrint publication year: 2013