GE 331-Lecture 6

# GE 331-Lecture 6 - Discrete Random Variables IE 300/GE 331...

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IE 300/GE 331 Lecture 6 Negar Kiyavash, UIUC 1 Discrete Random Variables

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IE 300/GE 331 Lecture 6 Negar Kiyavash, UIUC 2 Motivation The outcomes of an experiment can be numerical or not numerical Not numerical: Flip a coin: outcomes are H or T Numerical: The height of a randomly selected student If we select multiple students what is the average height? What if we flip the coin multiple times?
IE 300/GE 331 Lecture 6 Negar Kiyavash, UIUC 3 Motivation (cont) We know how to deal with numerical values: calculus Definition of probability theory: calculus of uncertainty We need to quantify uncertain outcomes in a way that we can perform calculations Any ideas how to do this?

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IE 300/GE 331 Lecture 6 Negar Kiyavash, UIUC 4 Motivation (cont) What if there was a way of mapping the outcomes to numerical values. sample space Ω Real number line A random variable is a real-valued function of the outcome of the experiment
IE 300/GE 331 Lecture 6 Negar Kiyavash, UIUC 5 Motivation (cont) Formally, a random variable is a function whose domain is the sample space Ω and whose co-domain is the real line In everyday language, a random variable assigns a real number to each outcome in the sample space Ω The random variable is said to map an outcome to its assigned real number X maps w є Ω to the number X(w)

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## This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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GE 331-Lecture 6 - Discrete Random Variables IE 300/GE 331...

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