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Lecture24_FinalReview

# Lecture24_FinalReview - ECE 340 Probabilistic Methods in...

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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 19: Sums of RV Lecture 19: Sums of RV s, Sample s, Sample Mean, Laws of Large Numbers Mean, Laws of Large Numbers

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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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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 21: Hypothesis Testing 1 Lecture 21: Hypothesis Testing 1
Confidence Interval Confidence interval on mean, variance known If: random sample of size n: X 1 , …, X n X i ~ N( μ , σ 2 ) and X ~ N( μ , σ 2 /n) Then the test statistic: n X Z / 2 σ μ = ~ N(0, 1) by CLT With a CI, we want some range on μ , P[-Z α /2 Z Z α /2 ] = α , P[-Z α /2 n X / σ μ Z α /2 ] = 1- α probability test statistic between 2 points is 1- α

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Confidence Interval P[-Z α /2 n / σ μ X Z α /2 n / σ ] = 1- α want a range on μ P[- X + (-Z α /2 n / σ ) - μ - X + (Z α /2 n / σ )] = 1- α P[ X + Z α /2 n / σ μ X - Z α /2 n / σ ] = 1- α P[ X - Z α /2 n / σ μ X + Z α /2 n / σ ] = 1- α a 100(1- α )% CI (2-sided) on μ is: X - Z α /2 n / σ μ X + Z α /2 n / σ or X ± Z α /2 n / σ A CI is a statistic ± (table value) x standard error.
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