lecture%202_s

lecture%202_s - APPENDIX B Fundamentals of probability 1...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
APPENDIX B Fundamentals of probability
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1. RANDOM VARIABLES An experiment is any procedure that can, at least in theory, be infinitely repeated and has a well-defined set of outcomes . E.g. flip a coin thrice and record the number of times the coin turns up heads. A random variable is a variable that takes on numerical values and the values that a random variable can take are determined by an experiment. E.g. in the coin- flipping experiment, the number of heads that appear in 3 flips of a coin is an example of a random variable. Why is it called a random variable? Because before the experiment is conducted, the value of the random variable is unknown. It is only after conducting the experiment that we obtain the value/outcome of the random variable for that particular trial of the experiment. Another trial can produce a different outcome. Random variables are denoted by uppercase letters, usually W, X, Y and Z . Particular outcomes of random variables are denoted by the corresponding lowercase letters, w, x, y and z .
Background image of page 2
1. RANDOM VARIABLES The properties of a random variable can be described by its sample space and its probability distribution over the sample space. The set of all possible outcomes/values for the random variable is called the sample space . The outcomes can be discrete or continuous. The likelihood of a RV taking any given value in the sample space is governed by the probability distribution of the RV. The probability that a RV takes a particular value from the sample space has the following properties: The probability that a RV takes any single value in the sample space has to be between 0 and 1. All the probabilities must sum to 1. A random variable can be fully characterized by its probability density function (pdf). The pdf of a random variable summarizes the information concerning the possible outcomes of the RV and the corresponding probabilities. Its denoted by: ? ? ° = ? ° = ±(? = ? ° )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A discrete random variable is one that takes on only a finite number of values. Simple example: Experiment: “Tossing a single coin” There are only 2 (i.e. discrete) possible outcomes: a head or a tail. Assumption: it is a “fair” coin i.e. the probability that a head occurs is equal to the probability that a tail occurs and equal to 0.5. We define a random variable X : X=1 if the coin turns up heads, and X=0 if the coin turns up tails. Sample space
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 27

lecture%202_s - APPENDIX B Fundamentals of probability 1...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online