Statistics 2

Probability:

• Set theory: the basics Axiomatic definition of probability
• Classical probability and counting rules
• Conditional probability and Bayes’ theorem.

Random variables:

• Discrete random variables
• Continuous random variables.

Common distributions of random variables:

• Common discrete distributions
• Common continuous distributions.

Multivariate random variables:

• Joint probability functions
• Conditional distributions
• Covariance and correlation
• Independent random variables
• Sums and products of random variables.
• Sampling distributions of statistics: Random samples
• Statistics and their sampling distributions
  

   

Sampling distribution of a statistic

• Sample mean from a normal population
• The central limit theorem Some common sampling distributions
• Prelude to statistical inference.

Point estimation:

• Estimation criteria: bias, variance and mean squared error
• Method of moments estimation
• Least squares estimation
• Maximum likelihood estimation.
•  

Interval estimation:

• Interval estimation for means of normal distributions
• Use of the chi-squared distribution
• Confidence intervals for normal variances.

Hypothesis testing:

• Setting p-value, significance level, test statistic t tests
• General approach to statistical tests
• Two type of error
• Tests for normal variances
• Comparing two normal means with paired observations
• Comparing two normal means
• Tests for correlation coefficients
• Tests for the ratio of two normal variances

Analysis of variance:

• One-way analysis of variance
• Two-way analysis of variance.

Linear regression:

• Simple linear regression Inference for parameters in normal regression models;
• Regression ANOVA;
• Confidence intervals for E(y);
• Prediction intervals for y;
• Multiple linear regression models