LEC20 Sample Averages

# LEC20 Sample Averages - Sample Averages X i i = 1.n...

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Unformatted text preview: Sample Averages X i , i = 1...n independent identically distributed (iid) random variables from a population with mean μ and standard deviation σ Sample Average is a random variable! r.v. X X X n n = + + 1 .... • The mean and variance of the average E X n n V X n n n ( ) ... ( ) ... = + + = = + + = 1 1 1 1 2 2 2 2 2 μ μ μ σ σ σ Learn by heart: E X SD X n ( ) ( ) = = μ σ Example • Under regular production, each candy weight is normally distributed with mean 1.45 and std dev .02 ounces. Each day a sample of 12 candies is randomly selected and the average weight is computed. X N mean X N mean i ≈ = ≈ = ( ) ( ) 1.45, var =.0004, sd =.02 1.45, var =.0004 /12 =.0000333, sd =.006 • Sketch the distribution of individual candy weights. • Sketch the distribution of daily averages. • If a daily average is 1.47, what would you do? Is the production system operation as usual? 2 Central Limit Theorem : Averages and Sums of ANY iid Random Variables are Normal • Components have exponential lifetimes.Components have exponential lifetimes....
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LEC20 Sample Averages - Sample Averages X i i = 1.n...

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