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Unformatted text preview: Matthew J. Botsch 1 Dept. of Economics, UC Berkeley Ec 140 Fall 2011 (Duncan) Probability & Statistics Review Basic Concepts from Probability Random variable Bernoulli r.v. Uniform r.v. Normal or Gaussian r.v. 2 Expected Value and Variance Let X, Y, and Z be random variables, and a and b real numbers. The following properties of expectation, variance, and covariance will prove useful: Properties of Expected Values: 1. E[X+Y] = 2. E[XY] (in general) 3. E[aX] = Variance and Covariance: 1. Cov(X, X) = 2. Suppose X and Y are independent. Then Var(X + Y) = 3. Suppose X and Y are not independent. Then Var(X + Y) = 4. Cov(X, Y + Z) = 5. Var(aX + b) = 6. Cov(aX, bY) = 7. Correlation(X, Y) = Expectation is easy because it is a ____________ ______________. Covariance is a ______________ ______________. This means that it is linear in ___________ _______________. Two Convenient Formulas You can prove these formulas by working directly from the definitions, then adding and subtracting a term and simplifying. These turn out to be very useful in a variety of applications!...
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- Spring '08