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Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. Joint Desity. The density function f(x,y) for a pair of RVs X and Y is the density of probability per area of ( X,Y ) near ( x,y ). Joint Desity. Densities single variable bivariate norm.

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356 views • 25 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. Sampling with replacement. Suppose we have a population of size N with G good elements and B bad elements . We draw n times with replacement from this population.

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172 views • 17 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. # of Heads in a Random # of Tosses. Suppose a fair die is rolled and let N be the number on top. N=5. Next a fair coin is tossed N times and H , the number of heads is recorded:. H=3. Question :

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171 views • 17 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. # of Heads in a Random # of Tosses. Suppose a fair die is rolled and let N be the number on top. N=5. Next a fair coin is tossed N times and H , the number of heads is recorded:. H=3. Question :

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290 views • 16 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. Multiplication rule for 3 Events. The Multiplication rule for two events says: P(AB) = P(A) P(B | A) The Multiplication rule extends to 3 Events: P(ABC) = P(AB)P(C | AB) = P(A) P(B | A) P(C | AB). A c. B c. C c. P(A). P(B|A). P(C|AB).

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165 views • 16 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. Do taller people make more money?. Question : How can this be measured?. -. Ave (height). wage at 19. Ave (wage). height at 16. National Longitudinal Survey of Youth 1997 (NLSY97). Definition of Covariance.

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335 views • 15 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. Bivariate Normal. Let (X,Y) be independent Normal variables. r = 0;. y. x. Bivariate Normal. Question: What is the joint distribution of ( X,Y ) Where X = child height and Y = parent height ?

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153 views • 15 slides
Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets

Lectures prepared by: Elchanan Mossel Yelena Shvets. B. D. B. P((X,Y) 2 B) =. D. Uniform distribution in an area. Y. Sample space is D. Outcomes are points in D with random coordinates (X,Y). ). X. Area(. A. Area(. ). Probability of each subset is equal to its relative area.

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143 views • 7 slides

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