economics formulas cheat sheet, Cheat Sheet of Economics

Download economics formulas cheat sheet and more Cheat Sheet Economics in PDF only on Docsity! Economics 250 Formula Sheet Descriptive Statistics Population Sample Mean μ = 1N ∑N i=1 xi x = 1 n ∑n i=1 xi Variance σ2 = 1N ∑N i=1(xi − μ)2 s2 = 1n−1 ∑n i=1(xi − x)2 CV σμ × 100 sx × 100 Covariance σxy = 1N ∑N i=1(xi − μx)(yi − μy) sxy = 1n−1 ∑n i=1(xi − x)(yi − y) Correlation ρxy = σxy σxσy rxy = sxy sxsy Grouped Data With K classes, with midpoints mi and counts ci, the sample mean is x = 1n ∑K i=1 cimi, and the sample variance is s2 = 1n−1 ∑K i=1 ci(mi − x)2, where n = ∑K i=1 ci. 68–95–99.7 Rule For a normal distribution 68% of the observations are in μ ± 1σ, 95% are in μ ± 2σ, and almost all (99.7%) are in μ ± 3σ. Normal Distribution For −∞ < x < ∞ f(x) = (2πσ2)−1/2 exp [−(x − μ)2 2σ2 ] with mean μx and standard deviation σx, then x ∼ N(μx, σx) z = x − μx σx ∼ N(0, 1) Warning: Some people record the normal distribution as N(μx, σ2x) i.e. the second number in brackets is the variance rather than the standard deviation. Uniform Distribution For a ≤ x ≤ b f(x) = 1 b − a E(x) = a + b 2 V ar(x) = (b − a)2 12 Random Variables Let x be a discrete random variable, then: μx = E(x) = ∑ x xP (x) 1 σ2x = ∑ x (x − μ)2P (x) The covariance of x and y is: cov(x, y) = σxy = E(x − μx)(y − μy) = ∑ x ∑ y (x − μx)(y − μy)P (x, y) The correlation between x and y is: ρxy = σxy σxσy For a continuous rv replace the sums by integrals. Functions of Random Variables If y = a + bx then: E(y) = μy = a + bμx, and σ2y = b 2σ2x. If w = cx + dy then: E(w) = μw = cμx + dμy, and σ2w = c 2σ2x + d 2σ2y + 2cdσxy. Sampling Distribution of the Sample Mean For large samples, x ∼ N(μ, σ√ n ) Probability Theory P (A) = 1 − P (A) (complement rule) P (A ∪ B) = P (A) + P (B) − P (A ∩ B) (addition rule) P (A ∩ B) = P (A|B)P (B) (multiplication rule) A and B are independent if P (A ∩ B) = P (A)P (B) Marginal probabilities add entries in a joint probability table. If Bi are mutually exclusive and exhaustive events then: P (A) = n∑ i=1 P (A ∩ Bi) Bayes’s Rule: P (B|A) = P (A|B)P (B) P (A) 2