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# ioe265f11-Lec06 - Lec06 Discrete Random Variables Topics...

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Lec06 - Discrete Random Variables IOE 265 F11 1 1 Discrete Random Variables and Distributions 2 Topics I. Random variables Definition Types II. Probability distributions for discrete random variables Probability mass function Cumulative distribution function III. Expected values of discrete random variables Expected values (r.v., function, rules) Variance (r.v., rules)

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Lec06 - Discrete Random Variables IOE 265 F11 2 3 I. Random variables Definition: A random variable (rv) is a rule that associates a value with each of the possible outcomes of an event Example: if X is a random variable that defines the number of heads that we may obtain when we flip 3 coins, then X can take 4 values: 0,1,2,3 4 Bernoulli random variables A random variable (rv) whose values are only 0 or 1 is called a Bernoulli random variable Common Notation: 0 – Fail (F); 1 – Success (S) Example: Suppose X is a random variable that indicates whether a user can login to a computer system, either all ports are busy (Fail) or there is at least one port free (Success), then X can take 2 values 0 or 1: X (S)=1, X (F)=0
Lec06 - Discrete Random Variables IOE 265 F11 3 5 Discrete and Continuous rv A discrete rv has whole unit values either in a finite set or listed in an ascending infinite sequence (first element, second element, and so on) Example: X is discrete rv defined by the # of pumps in use at a gas station A continuous rv takes any value in a given interval. It has an infinite (or nearly infinite) set of possible values. Example: Z is a rv defined by Z =the speed at which a professional tennis player hits his/her first serve 6 Exercise 1 Let X =the number of nonzero digits in a randomly selected zip code. What are the possible values of X ? Give three possible outcomes and their associated X values

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Lec06 - Discrete Random Variables IOE 265 F11 4 7 Different rv’s from the Same Sample Space Gas Station Example: Two Stations: #1 ~ 6 pumps; #2 ~ 4 pumps Possible rv’s to study T = Total # of pumps in use
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## This note was uploaded on 01/05/2012 for the course IOE 265 taught by Professor Jin during the Fall '07 term at University of Michigan.

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ioe265f11-Lec06 - Lec06 Discrete Random Variables Topics...

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