This module builds on the material covered in MATH 1805 to include jointly distributed random variables, moments of random variables and moment generating functions and introduces the mathematics of statistical sampling theory and inference.
Properties of expectation and variance. Moments of the standard discrete and continuous probability distributions. Moment generating functions; properties and uses.
Jointly Distributed Random Variables:
Jointly distributed discrete and continuous random variables. The expected value of functions of two or more random variables. Independence. Covariance and correlation.
The Central Limit Theorem. Estimation: Confidence intervals and their interpretation based on the Central Limit Theorem, small sample intervals (chi-squared & t-distributions).
Null and alternative hypotheses. P-values and their use. Types I and II errors. Z, chi-squared and t tests for single sample and two sample data. Chi-squared tests for contingency tables.
Lectures supported by tutorials and computer laboratory sessions.
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