I&C SCI 6D Lecture Notes - Lecture 11: Bijection, Uncountable Set, Lexicographical Order

• School: UC-Irvine
• Department: Information and Computer Science
• Course: I&C SCI 6D
• Professor: Sandra Irani

Document Summary

An experiment is a procedure that results in one out of number of possible outcomes. The set of all possible outcomes is called the sample space of the experiment. A subset of the sample space is called an event. Discrete probability is concerned with experiments in which the sample space is a finite or countably infinite set. A set is countably infinite if it can be shown to have a one-to-one correspondence with the integers. Set of all binary strings (of any length), the set of ordered pairs of integers (z x z), the set of all rational numbers. The set of real numbers of an example of an uncountably infinite set. The set of real numbers in a finite interval is also not countable because are a lot of uncountable irrational numbers in that set. The probability distribution in which every outcome has the same probability is called the uniform distribution.