This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 5 PROBABILITY CONTINUED: DISCRETE RANDOM VARIABLES 5.1 Discrete random variables Devore 7e: Sections 3.1, 3.2 Range, pmf, cdf 5.2 Expectation, mean and variance Devore 7e: Section 3.3 5.3 Several random variables Devore 7e: Pages 1856 Joint pmf , marginal pmf , independence 5.4 Examples of discrete random variables Devore 7e: Sections 3.43.6 Discrete uniform, binomial, negative binomial, geometric, Poisson, hypergeometric 5.5 Chebyshevs Inequality Devore 7e: Pages 1078 (Exercise 44). 1 5.1. RANDOM VARIABLES Random variable : A rule that assigns a real number to each outcome in the sam ple space. See Figure 3.1 of Devore 7e for pictorial representation. Range R : set of possible values that the random variable can take on. Notation: We typically use upper case letters to denote random variables. We use lower case letters to denote a particular value that a random variable X takes on. For example, if basic outcome o occurs and X(o) = x , say, then we say the event { X = x } has occurred. Of course x must be a member of R . This is best understood through examples. Shorthand: event {X = x} = {o: X(o) = x} . Example: Toss 2 dice: X = sum { X = 4} = {(1,3), (2,2), (3,1)}. Discrete random variable : X only takes on discrete values. Example: X = No. of tosses till first head appears. R = {1,2,3,. . . }. Probability mass function ( pmf ) f(x) = P[X = x] (Note: Devore uses the notation p ( x ) rather than f ( x ) .) Properties f ( x ) , x R f ( x ) = 1 Cumulative distribution function (cdf) F ( x ) = P [ X x ] = X x x x R f ( x ) Increasing step function, F ( ) = 0 , F (+ ) = 1 2 Example: Geometric random variable Coin tossing: P (head) = p P (tail) = 1 p = q....
View
Full
Document
This note was uploaded on 02/13/2008 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 STAFF

Click to edit the document details