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

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

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O tli Outline Random Variable Discrete & Continuous P b bilit Di t ib ti Probability Distribution Expected Value & Variance f S Linear Transformation & Standardization 2
D fi iti R d V i bl Definition: Random Variables A function or rule that assigns a number to each outcome of 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: Di d C i Discrete and Continuous A Discrete Random Variable takes countable(finite) number of values. Example: Experiment1 Roll a die twice and add outcomes Example: Experiment1 – Roll a die twice and add outcomes. There are 11 possible values X can take. A C ti R d V i bl k l h Continuous Random Variable takes values that are uncountable(infinite). Example: The speed of randomly sampled 100 automobiles at a point on Don Valley Parkway between 7am and 8am on M d Monday.
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