1. The Erik Jonsson School of Engineering and Computer Science Chapter 6 pp. 243-274 William J. Pervin The University of Texas at Dallas Richardson, Texas 75083

2. The Erik Jonsson School of Engineering and Computer Science Chapter 6 Sums of Random Variables

3. The Erik Jonsson School of Engineering and Computer Science Chapter 4 6.1 Expected Values of Sums: E[ΣX i ] = ΣE[X i ] Var[ΣX i ] = ΣVar[X i ] + ΣΣ (i≠j) Cov[X i,X j ]

4. 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

5. 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

6. The Erik Jonsson School of Engineering and Computer Science Chapter 6 6.3 Moment Generating Functions: The MGF Φ X of a RV X is the transform Continuous: Φ X (s) = ∫e sx f X (x)dx Discrete: Φ X (s) = Σe sx i f X (x i )

7. The Erik Jonsson School of Engineering and Computer Science Chapter 6 The sum of independent Poisson/Gaussian RVs is a Poisson/Gaussian RV.

8. 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!