# Mathematical Statistics I

University of Cape Town

## Course Description

• ### Course Name

Mathematical Statistics I

• ### Host University

University of Cape Town

• ### Location

Cape Town, South Africa

• ### Area of Study

Mathematics, Statistics

• ### Language Level

Taught In English

• ### Prerequisites

Course entry requirements: At least 70% in NSC Mathematics; concurrent registration on MAM1000W, or MAM1006H or MAM1012S.

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

18
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4 - 5
• ### Overview

Course outline:
This is an introduction to statistics: the study of collecting, analysing, and interpreting data. It is the key entry-point into a Mathematical Statistics major and hence it is compulsory for students intending to major in Mathematical Statistics. This course provides foundation knowledge in statistical theory, and is useful for any student who wishes for an introduction to the fundamentals of statistics, from a mathematical perspective. Topics covered include: Types of data variables. Exploratory data analysis. Grouping and graphing of data. Set theory and counting rules. Probability: conditional probabilities, independence. Bayes theorem. Random variables and values, probability mass and density functions, cumulative distribution functions. Population models and parameters: binomial, poisson, geometric, negative binomial, hypergeometric. Uniform, exponential,
Gaussian, expectation. Coefficient of variation. Sampling: sampling distribution t, Chi-square, F and their tables. Point and interval estimation. Sample size estimation. Hypotheses testing: Z-test and T-test (means, difference between means: for independent samples and dependent samples). F-test (ratio of two independent variances). Chi-square-test. Meaning of p-values. Bivariate data: scatterplot, simple linear regression and correlation.

### Course Disclaimer

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.