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  1. Why this is the most important course in the degree
  2. Two things you must know before you start
  3. Course objectives (verbatim)
  4. Units in this Course

Why this is the most important course in the degree

Strip away the programming and data science is statistics. Every model you meet later — Data Mining, Machine Learning, Time Series — is applied statistics with a library wrapped around it.

A model that reports 95% accuracy on a dataset where 95% of cases are one class has learned nothing. Knowing that is statistics, not programming. This course is where you learn to tell a real result from a plausible-looking one.

Two things you must know before you start

1. Bayes' theorem is examined but is not in the syllabus units. Unit 1 lists only "conditional probability". Bayes appears in the prescribed activities quiz and in lab experiment 2 — but never as a unit topic. Study it anyway; it is covered in unit-1.md. See SYLLABUS-REVIEW.md finding D1.

2. The lab never uses Python. All 15 experiments are Excel/PSPP, even though Python Programming and Data Structures teaches the language. Do them in Excel for the exam and again in Python for the skill — both versions are provided. See finding D8.

Course objectives (verbatim)

  1. To introduce the fundamental concepts of probability and statistics for quantifying and analyzing uncertainty in real-world problems.

  2. To develop an understanding of random variables, expectations, and common probability distributions.

  3. To build the ability to summarize and describe data using measures of central tendency, dispersion, correlation, and visualization.

  4. To equip students with statistical tools for modeling relationships using correlation and regression analysis.

  5. To provide knowledge of estimation and hypothesis testing for making valid inferences from sample data about populations.

Units in this Course

UNIT 1

Fundamentals of Probability and Basic Statistics

Axioms and rules of probability, conditional probability and Bayes' theorem; central tendency, dispersion, correlation and covariance.

 UNIT 2

Random Variables, Expectation and Variance

Discrete and continuous random variables, PMF, PDF and CDF; expectation, variance, moments and the MGF.

 UNIT 3

Probability Distributions

Binomial, Poisson, geometric, negative binomial; uniform, normal, exponential, gamma; joint distributions and the Central Limit Theorem.

 UNIT 4

Correlation and Regression

Bivariate data, Pearson and Spearman correlation; simple linear regression, ANOVA, residuals and goodness of fit.

 UNIT 5

Statistical Inference, Estimation and Hypothesis Testing

Sampling distributions, confidence intervals; z, t, chi-square and F tests; p-values, Type I and II errors and power.

 PRACTICE

Practice

Exam-style questions with fully worked solutions.

 LAB

Lab

Every prescribed lab experiment, with code and expected output.

 REFERENCE

Formula Sheet

Every formula from the five units on one page for revision.
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