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Unformatted text preview: 1. Introduction & Review (Appendices & chapter 1) Math, Probability, Stats Review Constant – something that does not change Variable – something that takes on different values for different observations Parameters – constants that define the direction & strength of a relationship between variables. Basic Math summation operator : ∑ i = 1 n x i = x 1 x 2 ... x n Properties of Summation Operator For any constant c: ∑ i = 1 n c = nc For any constant c: ∑ i = 1 n cx i = c ∑ i = 1 n x i For any constants a and b, and variables x and y: ∑ i = 1 n ax i by i = a ∑ i = 1 n x i + b ∑ i = 1 n y i be careful! ∑ i = 1 n x i y i ≠ ∑ i = 1 n x i / ∑ i = 1 n y i Some Statistics using Basic Math mean of a variable: x = n − 1 ∑ i = 1 n x i Deviation from the mean: d i = x i − x Sum of deviations: ∑ i = 1 n d i = ∑ i = 1 n x i − x = ∑ i = 1 n x i − ∑ i = 1 n x = 0 Variance: 1 n ∑ i = 1 n x i − x 2 = 1 n ∑ i = 1 n x 2 − 2x i x x 2 = 1 n ∑ i = 1 n x i 2 − x 2 Linear Functions : y = x y is a linear function of the variable x. The parameters (constants) are and . y y = x slope = = y x y = x ∂ y /∂ x = = marginal effect of x on y (constant) x proportional change = relative change = x 1 − x / x = x / x precentage change = 100* proportional change =change Properties of the natural log function ln ab = ln a ln b ln a / b = ln a − ln b ln a b = b ln a ln b a = ln a / b ln e x = x ln 1 x ≈ x forsmallx d [ ln x ]/ dx = 1 / x log b x = ln x / ln b careful! ln a b ≠ ln a ln b Properties of the exponents e = 1 e 1 = e e ln x = x b p = e p ln b e x y = e x e y e xy = e x y 1 / e x = 1 / e x = e − x a x b x = ab x 1 / a = a − 1 d / dx e x = e x d /...
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.
 Fall '08
 Burbidge,John

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