APMA 3100 Study Guide - Final Guide: Central Limit Theorem, Uncorrelated Random Variables, Random Variable

• School: University of Virginia
• Department: Applied Mathematics
• Course: APMA 3100
• Professor: Fulgham Bernard

Document Summary

Page 1: conditioning a random variable given an event b with p [b] > 0 (a) (section 2. 9) discrete: (b) (section 3. 8) continuous: 0 otherwise: conditional expected value of a function of a random variable given an event b (a) (section 2. 9) discrete: (b) (section 3. 8) continuous: For x b, e [g(x)|b] =& g(x) fx|b(x) dx: conditional variance of a random variable given an event b (a) (sections 2. 9, 3. 8 and 4. 8) V ar [x|b] = e[x 2|b] (e[x|b])2: two variable joint cdf, pmf and pdf (a) (section 4. 1) (b) (section 4. 2) (c) (section 4. 4, marginal pmfs and pdfs (a) (section 4. 3) discrete: (b) (section 4. 5) continuous: Fx,y (x, y) = p [x x, y y] =& x. Px,y (x, y) = p [x = x, y = y] fx,y (x, y) = 2fx,y (x, y) Px,y (x, y) fx,y (x, y) dy and py (y) = %x sx fy (y) =& and.