Outline of IB Mathematics HL - Option: Statistics and probability

Here you can find a description of the course not so detailed.

You can find the official syllabus of IB maths SL on the following link of IBO

http://www.ibo.org or http://store.ibo.org

Cumulative distribution functions for both discrete and continuous distributions. Geometric distribution.

Negative binomial distribution. Probability generating functions for discrete random variables.

Using probability generating functions to find mean, variance and the distribution of the sum of n independent random variables.

Linear transformation of a single random variable. Mean of linear combinations of n random variables. Variance of linear combinations of n independent random variables.

Expectation of the product of independent random variables.

Unbiased estimators and estimates. Comparison of unbiased estimators based on variances.

Unbiased estimator for μ, unbiased estimator for .

A linear combination of independent normal random variables is normally distributed. The central limit theorem.

Confidence intervals for the mean of a normal population. Null and alternative hypotheses, and .

Significance level. Critical regions, critical values, p-values, onetailed and two-tailed tests.

Type I and II errors, including calculations of their probabilities. Testing hypotheses for the mean of a normal population.

Introduction to bivariate distributions. Covariance and (population) product moment correlation coefficient ρ.

Definition of the (sample) product moment correlation coefficient R in terms of n paired observations on X and Y. Its application to the estimation of ρ.

Informal interpretation of r, the observed value of R. Scatter diagrams. The following topics are based on the assumption of bivariate normality.

Use of the t-statistic to test the null hypothesis. Knowledge of the facts that the regression of X on Y and Y on X are linear.Least-squares estimates of these regression lines. The use of these regression lines to predict the value of one of the variables given the value of the other.