# lecture11 - ECO ECO 220Y Random Variables and Probability...

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ECO 220Y Lecture 11 Random Variables and Probability Distributions Migiwa Tanaka Readings: 7.1 1

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Outline andom Variable Random Variable Discrete & Continuous b bilit i t ib ti Probability Distribution Expected Value & Variance Linear Transformation & Standardization 2
Definition: Random Variables A function or rule that assigns a number each outcome of u ct o o u e t at ass g s a ub e to eac outco e o an experiment. Experiment1 – Roll a die twice and add outcomes. Sample Space= {2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12} Random variable X can take values between 2 to 12 Example II – Randomly take one part from 1000 parts in the factory and check if it is defective Sample Space={Defective, Good} Assign 1 to defective and 0 to good. Random variable X takes a value either 1 or 0. Are following random variables? Population mean Sample statistics 3

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Types of Random Variables: Discrete and Continuous iscrete Random Variable kes countable(finite) A Discrete Random Variable takes countable(finite) number of values. xample: Experiment1 oll a die twice and add outcomes Example: Experiment1 – Roll a die twice and add outcomes. There are 11 possible values X can take. A Continuous Random Variable takes values that are uncountable(infinite).
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## This note was uploaded on 03/01/2011 for the course ECON 220 taught by Professor Tanaka during the Spring '11 term at University of Toronto.

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lecture11 - ECO ECO 220Y Random Variables and Probability...

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