​Statistics

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Topic 1   Exploring further probability distributions

Learning objective:  Probability as a tool to make informed decisions

•  Cumulative distribution function
•  Discrete and continuous quantities
•  Geometric distribution
•  Expected value and variance of a geometric random variable
•  Negative binomial distribution
•  Probability generating functions
•  The sum of independent variables

 
 

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Topic 2   Expectation algebra and Central Limit Theorem

Learning objective:  Normal distributions and probability models

•  Expectation algebra
•  Linear transformation of a single variable
•  Linear transformation of two or more variables
•  A linear combination of independent normal random variables
•  Sampling distribution of the mean
•  The Central Limit Theorem

 
 
 
 

 
 
 
Topic 3   Exploring statistical analysis methods

Learning objective:   How can we make sense of data

•  Estimators and estimates
•  Unbiased estimators for the mean and variance of a normal random variable
•  Confidence interval for µ when σ is known
•  Confidence interval for µ when σ is unknown
•  Confidence interval for matched pairs
•  Hypothesis testing for µ when σ is unknown
•  Significance testing for matched pairs
•  Type I and Type II errors
•  Normal distribution graph for a one-tail test
•  Two-tail test

 



 
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Topic 4   Statistical modeling

Learning objective:  Bivariate distributions

• Correlation
• Correlation and causation
• Sampling distributions
• Covariance
• Properties of covariance
• Hypothesis testing
• t-Statistic for dependence of X and Y
• Linear regression