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Statistics 2 ST104b

Half course

This half course requires the student to develop the concepts introduced in ST104a Statistics 1 of measurement and hypothesis testing.

Prerequisites/ Exclusions

This course must be taken at the same time as or after:

  • ST104a Statistics 1.

Topics covered


  • 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.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments
  • Explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform tests in a number of different settings
  • Demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.


Unseen written examination (2 hr).

Essential reading

  • Newbold, P., W. Carlson and B. Thorne. Statistics for Business and Economics. London: Pearson.

Course information sheets

Download the course information sheets from the LSE website.