Lecture20_CentralLimitSamplingParameter

# Lecture20_CentralLimitSamplingParameter - ECE 340...

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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 20: Central Limit Theorem Lecture 20: Central Limit Theorem

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Quiz • Write down (or compute) the mean and variance of the sample mean for iid random variables with mean m x and variance σ 2 • True or False: The Strong Law of Large Numbers refers to convergence in probability
• Section 7.3 • Central Limit Theorem

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Statistical inference – process by which information from samples data is used to draw conclusions about the population from which the sample was selected.

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Central limit theorem If X is the mean of a random sample X 1 , …, X n, of size n from a distribution with finite mean μ and finite positive variance σ 2 , then the distribution of: σ μ n n T n X W o = = is N(0,1) as n . Important points to notice: o When n is “sufficiently large” (n>30), a practical use of the CLT is : () w dz e w W P z w Φ = 2 2 2 1 π o The theorem holds for any distribution with finite mean and variance.
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Lecture20_CentralLimitSamplingParameter - ECE 340...

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