Introduction to probability and statistical inference

Course contents

• Rules and axioms of probability theory and the probability distribution of a discrete and continuous random variable
• Density and cumulative distribution function, expected value, variance and standard deviation
• Uniform distributions, Bernoulli, binomial and Poisson distributions
• Normal distribution, t-, F- and chi^2 distributions
• Joint probability distribution, covariance, correlation, random sample, sample statistic, distribution of the statisticpoint and confidence interval estimation
• Principles of hypotheses testing, estimation and testing under Bernoulli and normal distributions

Learning outcomes

After the course, the student

• has learned the basic rules of calculating the probabilities and the basics of combinatorics
• understands the concept of a random variable and knows the properties of expectation and variance
• is familiar with the most often used discrete and continuous probability distributions and is able to perform probability calculations under these distributions
• understands the concept of joint probability distribution and knows the properties of covariance and correlation
• obtains an understanding how random sampling is used in statistical inference, and why the concept of sample statistic and the distribution of the statistic are important in inference
• has learned the basic principles of estimation and hypothesis testing theory and is able to calculate confidence interval estimates and to perform statistical hypotheses testing especially in situations of one and two groups
• understands the limitations of the testing theory and is able to calculate different effect size measures.

Completion methods

Self-study and exam.

More information in the Tampere University study guide.

You can get a digital badge after completing this course.

matematiikka tilastotiede probability calculus