Exam 2 - crib sheet

# Exam 2 - crib sheet - Crib Sheet for Exam#2 Statistics 211...

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Crib Sheet for Exam #2 Statistics 211 1 Chapter 5: Joint Probability Distributions Marginal probability mass/density function: p X ( x ) = X Y p ( x, y ) p Y ( y ) = X X p ( x, y ) f X ( x ) = Z -∞ f ( x, y ) dy f Y ( y ) = Z -∞ f ( x, y ) dx Two RV X, Y are independent if for every pair of X, Y : p ( x, y ) = p X ( x ) · p Y ( y ) f ( x, y ) = f X ( x ) · f Y ( y ) otherwise they are dependent. Conditional probability density function of Y given that X = x is: f Y | X ( y | x ) = f ( x, y ) f X ( x ) - ∞ < y < p Y | X ( y | x ) = p ( x, y ) p X ( x ) Expected values: E [ h ( X, Y )] = X x X y h ( x, y ) · p ( x, y ) E [ h ( X, Y )] = Z -∞ Z -∞ h ( x, y ) · f ( x, y ) dxdy Cov ( X, Y ) = E [( X - μ x )( Y - μ y )] = E [ XY ] - μ x μ y ρ x,y = Corr ( X, Y ) = Cov ( X, Y ) σ X σ Y - 1 ρ x,y 1 Central Limit Theorem (CLT) states that if our random variables X i have a dis- tribution with whose mean and variance exist and X 1 , X 2 , . . . , X n are a random

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Exam 2 - crib sheet - Crib Sheet for Exam#2 Statistics 211...

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