# Lecture17 - ECO 220Y Lecture 17 Sampling Distribution Part...

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ECO 220Y Lecture 17 ampling Distribution art 1 Sampling Distribution – Part 1 Migiwa Tanaka Reading:9.1 1

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Outline troduction Introduction Sampling Distribution Definition Approaches Obtaining Sampling Distribution Analytically Sampling Mean Sampling Median imitation of Analytical Approach Limitation of Analytical Approach 2
Introduction: Recap of Random Variables A random variable has Assignment rule of value to each possible outcome of a random experiment. robability assigned to all possible values/interval Probability assigned to all possible values/interval. Function of random variables and Y are random variables X and Y are random variables. Are they random variables? Z 1 =X+3 Z 2 =X+Y Z 3 =X 2 xpectation of random variables Expectation of random variables Are they random variables? E[X] E[X+Y] V[X]=E[(X-E[X]) 2 ] 3

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Introduction: Random Sample and Statistics random sample: collection of random variables drawn A random sample: collection of random variables drawn from the same population ti ti l l t d ith d l Statistic: a measure calculated with a random sample Examples: sample mean, sample variance, sample median, etc. Is statistic a random variable? Example: sample mean:  n X X X X n X 3 2 1 1 It has a list/interval of possible values & probability distribution. We can use this knowledge to make statement about the accuracy of mple statistic an estimate of opulation parameter a sample statistic as an estimate of population parameter . 4
Sampling Distribution - Approaches mpling Distribution: the probability distribution of Sampling Distribution: sample statistic istribution only due to sampling error Distribution only due to sampling error Assume there is no bias. ariance measures sampling noise Variance measures sampling noise. Depending on population, statistic, sample size, the distribution n be discrete or continuous can be discrete or continuous.

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Lecture17 - ECO 220Y Lecture 17 Sampling Distribution Part...

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