## Probability and Measure

#### Statistical Science 9914B

**Description:**This course is an introduction to probability and measure theory. Topics include : the construction of Lebesgue measure on [0,1] (also called real measure theory). Finite and countable product measures are needed to construct independent sequences of r.v.s on R. Various extension theorems on algebras of sets. Monotone theorems. Expectation and Lebesgue integration. Change of variables formula. Conditional expectation and conditional probability.

If time permits the construction of random vectors and stochastic processes are studied.

**Term:**B