Discrete Random Variables: PMFs and Moments Lemon Chapter 2 Intro to Probability 2.1-2.5.

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Presentation transcript:

Discrete Random Variables: PMFs and Moments Lemon Chapter 2 Intro to Probability

Basic Concepts  Random Variable:  Every outcome has a value (number) for its probability  Can be discrete or continuous values  More than one random variable may be assigned to the same sample space  e.g. GPA and height of students  5 tosses of a coin: number of heads is random variable  Two rolls of die: sum of two rolls, number of sixes in two rolls, second roll raised to the fifth power  Transmission of a message: time to transmit, number of error symbols, delay to receive message  Notation:  Random variable: X  Numerical value: x

Probability Mass Function (PMF)  How to Calculate PMF of random variable (for each possible value x) 1. Collect all possible outcomes that give rise to the event (X = x) 2. Add their probabilities to obtain p x (x)

More About Random Variables BernoulliBinomial

More About Random Variables GeometricPoisson

Functions of Random Variables

Moments: Expectation, Mean, and Variance

Joint PMFs  Combination of multiple random variables associated with the same experiment  Example 2.9 (pp )  This process can be extended to more than two random variables

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