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Lecture 17

Lecture 17,18 Pre.pdf

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Department
Statistics
Course Code
STAB22H3
Professor
Michael Krashinsky

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Pre-Lecture Seventeen and Eighteen ▯ De▯nition: A collection of random variables 1 ;X2;:::;Xnis called a sample if they are independent and identically distributed. ▯ Denote by X the sample mean of a sample X ;X ;1::;2 and dn▯ne it to be ▯ X 1 X +2▯▯▯ + X n X = n ▯ By virtue of being a function of unpredictable quantities, the sample mean is also unpredictable, ie the sample mean is itself a random variable. ▯ This begs several questions: { What are the mean and standard deviation of X?▯ ▯ { What is the distribution of X? ▯ ▯ Fact: If X is the sample mean of a sample X ;X1;:2:;X havnng common distribution with mean ▯ and standard deviation ▯ then X has mean ▯ also p but standard deviation ▯= n ▯ The Law of Large Numbers says that the sample mean would approach
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