# First Course in Probability and Statistics

- the notion of probability and its basic arithmetic rules

- the most important discrete and continuous distributions

- expectation, sample mean, and the law of large numbers

- variance, sample variances, and normal approximation

- stochastic dependence and correlation

- description of data using statistics and histograms

- parameter estimation of statistical models

- the concept of a confidence interval

- prior distribution, likelihood function, and posterior distribution

- testing of

- the most important discrete and continuous distributions

- expectation, sample mean, and the law of large numbers

- variance, sample variances, and normal approximation

- stochastic dependence and correlation

- description of data using statistics and histograms

- parameter estimation of statistical models

- the concept of a confidence interval

- prior distribution, likelihood function, and posterior distribution

- testing of

### Schedule:

–

### Teaching time:

Daytime

### Location:

Espoo

### Topic:

Mathematics

### Form of learning:

On-campus

### Provider:

Aalto University Open University

### Level:

Beginner

### Credits:

5 By Aalto University (ECTS)

### Fee:

€ 75.00

## Course description

After course the student

- can compute probabilities of composite events by applying operations of set theory

- is familiar with the most important discrete and continuous probability distributions and recognizes situations that can modeled with them

- can apply joint distributions to compute statistics of random vectors and to recognize when two random variables are stochastically independent

- knows methods for estimating the parameters of a statistical model

- can compute posterior distributions and make conclusions based on them

- can explain what can and what cannot be concluded from a p-value of chosen statistical test