review - Review of Probability and Statistics (i.e. things...

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Economics 20 - Prof. Anderson 1 Review of Probability and Statistics (i.e. things you learned in Ec 10 and need to remember to do well in this class!)
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Economics 20 - Prof. Anderson 2 Random Variables   X is a random variable if it represents a random draw from some population a discrete random variable can take on only selected values a continuous random variable can take on any value in a real interval associated with each random variable is a probability distribution
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Economics 20 - Prof. Anderson 3 Random Variables – Examples   the outcome of a coin toss – a discrete random variable with P(Heads)=.5 and P(Tails)=.5 the height of a selected student – a continuous random variable drawn from an approximately normal distribution
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Economics 20 - Prof. Anderson 4 Expected Value of X – E(X) The expected value is really just a probability weighted average of X E(X) is the mean of the distribution of X, denoted by μ x Let f(x i ) be the probability that X=x i , then = = = n i i i X x f x X E 1 ) ( ) ( μ
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Economics 20 - Prof. Anderson 5 Variance of X – Var(X) The variance of X is a measure of the dispersion of the distribution Var(X) is the expected value of the squared deviations from the mean, so ( 29 [ ] 2 2 ) ( X X X E X Var μ σ - = =
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Economics 20 - Prof. Anderson 6 More on Variance The square root of Var(X) is the standard deviation of X Var(X) can alternatively be written in terms of a weighted sum of squared deviations, because ( 29 [ ] ( 29 ( 29 - = - i X i X x f x X E 2 2 μ
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Economics 20 - Prof. Anderson 7 Covariance – Cov(X,Y) Covariance between X and Y is a measure of the association between two random If positive, then both move up or down together If negative, then if X is high, Y is low, vice versa ( 29 ( 29 [ ] Y X XY Y X E Y X Cov μ σ - - = = ) , (
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Economics 20 - Prof. Anderson 8 Correlation Between X and Y Covariance is dependent upon the units of Correlation, Corr(X,Y), scales covariance by the standard deviations of X & Y so that [ ] 2 1 ) ( ) ( ) , ( Y Var X Var Y X Cov Y X XY XY = = σ ρ
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Economics 20 - Prof. Anderson
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review - Review of Probability and Statistics (i.e. things...

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