Probability, Random Variables, And Random Proce... -

Probability provides a mathematical framework for quantifying uncertainty. It is built upon three main concepts: Sample Space (

): The set of all possible outcomes of a random experiment (e.g., for a coin toss). A subset of the sample space.

Take on any value within a range (e.g., temperature or time). Key Characteristics:

The rules that govern how probabilities are assigned, ensuring each probability is between 0 and 1 and that the total probability of the sample space is 1. 2. Random Variables (RV)

A random variable is a function that maps outcomes of a random experiment to real numbers.

Take on a countable number of values (e.g., the number of heads in 20 coin flips).

Measures of the "average" value and the "spread" of the RV. 3. Random Processes