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STA1610
Introduction to Statistics

5. Discrete probability distributions

← Bayes' theorem Random variables →

Discrete probability distributions

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Table of Contents

1. Data and statistics

1.1. Applications in business and economics
1.2. Data
1.3. Data sources
1.4. Descriptive statistics
1.5. Statistical inference
1.6. Analytics
1.7. Big data and data mining
1.8. Computers and statistical analysis

2. Descriptive statistics: tabular and graphical presentations

2.1. Summarizing categorical data
2.2. Summarizing quantitative data
2.3. Summarizing relationships between two categorical variables
2.4. Summarizing relationships between two quantitative variables

3. Descriptive statistics: numerical measures

3.1. Measures of location
3.2. Measures of variability
3.3. Measures of distributional shape, relative location and detecting outliers
3.4. Exploratory data analysis
3.5. Measures of association between two variables

4. Introduction to probability

4.1. Experiments, counting rules and assigning probabilities
4.2. Events and their probabilities
4.3. Some basic relationships of probability
4.4. Conditional probability
4.5. Bayes' theorem

5. Discrete probability distributions

5.1. Random variables
5.2. Discrete probability distributions
5.3. Expected value and variance
5.4. Bivariate distributions, covariance and financial portfolios
5.5. Binomial probability distribution
5.6. Poisson probability distribution
5.7. Hypergeometric probability distribution

6. Continuous probability distributions

6.1. Uniform probability distribution
6.2. Normal probability distribution
6.3. Normal approximation of binomial probabilities
6.4. Exponential probability distribution

7. Sampling and sampling distributions

7.1. The EAI sampling problem
7.2. Simple random sampling
7.3. Point estimation
7.4. Introduction to sampling distributions
7.5. Sampling distribution of X
7.6. Sampling distribution of P

8. Interval estimation

8.1. Population mean: s known
8.2. Population mean: s unknown
8.3. Determining the sample size
8.4. Population proportion

9. Hypothesis tests

9.1. Testing a population mean with s known: one-tailed test
9.2. Testing a population mean with s known: two-tailed test
9.3. Further discussion of hypothesis testing fundamentals
9.4. Population mean with s unknown
9.5. Population proportion
9.6. Type II errors and power

10. Statistical inference about means and proportions with two populations

10.1. Inferences about the difference between two population means: s1 and s2 known
10.2. Inferences about the difference between two population means: s1 and s2 unknown
10.3. Inferences about the difference between two population means: matched samples
10.4. Inferences about the difference between two population proportions

11. Inferences about population variances

11.1. Inferences about a population variance
11.2. Inferences comparing two population variances

12. Tests of goodness of fit and independence

12.1. Goodness of fit test: a multinomial population
12.2. Goodness of fit test: Poisson and normal distributions
12.3. Test of independence

13. Experimental design and analysis of variance

13.1. An introduction to experimental design and analysis of variance
13.2. Analysis of variance and the completely randomized design
13.3. Multiple comparison procedures
13.4. Randomized block design
13.5. Factorial experiment

14. Simple linear regression

14.1. Simple linear regression model
14.2. Least squares method
14.3. Coefficient of determination
14.4. Model assumptions
14.5. Testing for significance
14.6. Using the estimated regression equation for estimation and prediction
14.7. Computer solution
14.8. Residual analysis: validating model assumptions
14.9. Residual analysis: autocorrelation
14.10. Residual analysis: outliers and influential observations

15. Multiple regression

15.1. Multiple regression model
15.2. Least squares method
15.3. Multiple coefficient of determination
15.4. Model assumptions
15.5. Testing for significance
15.6. Using the estimated regression equation for estimation and prediction
15.7. Qualitative independent variables
15.8. Residual analysis
15.9. Logistic regression

16. Regression analysis: model building

16.1. General linear model
16.2. Determining when to add or delete variables
16.3. Analysis of a larger problem
16.4. Variable selection procedures

17. Time series analysis and forecasting

17.1. Time series patterns
17.2. Forecast accuracy
17.3. Moving averages and exponential smoothing
17.4. Trend projection
17.5. Seasonality and trend
17.6. Time series decomposition

18. Non-parametric methods

18.1. Sign test
18.2. Wilcoxon signed-rank test
18.3. Mann-Whitney-Wilcoxon test
18.4. Kruskal-Wallis test
18.5. Rank correlation

19. Index numbers

20. Statistical methods for quality control

21. Decision analysis

22. Sample surveys