STAB57H3 Lecture Notes - Lecture 12: Sample Space, Countable Set, Probability Axioms
Document Summary
Events are collections of points, i. e. subsets of rectangle. Intersection of a and b is set of all outcomes that are in both events. Probability function/measure is function that takes events and assigns probability values to sample spaces with distinct outcomes called discrete; can be. Roll of a die, toss of a coin countably infinite: elements can be put in 1-to-1 correspondence with natural numbers. Number of coin tosses before first head appears. For discrete s, probability function p is uniquely determined by the outcome probabilities. Finite spaces whose outcomes have equal probability are called (discrete) uniform probability spaces. Counting outcomes is essential for uniform probability there are three basic counting rules: Combination multiplication rule: with m elements {a. }, there are m n possible ordered pairs (a. How many 4-digit pin"s with unique (non repeated) digits are combinations (i. e. counting subsets) Combination: unordered collection of k objects chosen without repetition from n possible objects.
