Chapter 6 pp 243 274 William J Pervin
![Chapter 4 6. 1 Expected Values of Sums: E[ΣXi] = ΣE[Xi] Var[ΣXi] = ΣVar[Xi]](https://slidetodoc.com/presentation_image_h2/cd4e6448d3d3a6693564b11d5481f259/image-3.jpg "Chapter 4 6. 1 Expected Values of Sums: E[ΣXi] = ΣE[Xi] Var[ΣXi] = ΣVar[Xi]")
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Chapter 6 pp. 243 -274 William J. Pervin The University of Texas at Dallas Richardson, Texas 75083 The Erik Jonsson School of Engineering and Computer Science
Chapter 6 Sums of Random Variables The Erik Jonsson School of Engineering and Computer Science
Chapter 4 6. 1 Expected Values of Sums: E[ΣXi] = ΣE[Xi] Var[ΣXi] = ΣVar[Xi] + ΣΣ(i≠j)Cov[Xi, Xj] The Erik Jonsson School of Engineering and Computer Science
Chapter 6 6. 2 PDF of the Sum of Two RVs: The PDF of W = X + Y is: f. W(w) = ∫f. X, Y(x, w-x)dx = ∫f. X, Y(w-y, y)dy The Erik Jonsson School of Engineering and Computer Science
Chapter 6 If X and Y are independent RVs, then the PDF of W = X + Y is f. W(w) = ∫f. X(w-y)f. Y(y)dy = ∫f. X(x)f. Y(w-x)dx = f. X * f. Y : the convolution The Erik Jonsson School of Engineering and Computer Science
Chapter 6 6. 3 Moment Generating Functions: The MGF ΦX of a RV X is the transform sx Continuous: ΦX(s) = ∫e f. X(x)dx sxi Discrete: ΦX(s) = Σe f. X(xi) The Erik Jonsson School of Engineering and Computer Science
Chapter 6 The sum of independent Poisson/Gaussian RVs is a Poisson/Gaussian RV. The Erik Jonsson School of Engineering and Computer Science
Chapter 6 6. 6 Central Limit Theorem: The CDF of the sum of any number n of iid RVs approaches the Gaussian CDF with the same mean and variance as n increases! The Erik Jonsson School of Engineering and Computer Science
