chapter 7 conditional probability models - korea...
TRANSCRIPT
Chapter 7Conditional Probability Models
Chang-Su KimKorea University
These notes are modified from the files, provided by R. D. Yates and D. J. Goodman who are the authors of the textbook “Probability and Stochastic Processes,” and can be used only for the class KECE209(03) in Korea University.
Terminology Using a Dice Example
Sample space: 𝑆𝑆𝑋𝑋 = 1, 2, 3, 4, 5, 6Event: 𝐵𝐵 = 2, 4, 6 ⊂ 𝑆𝑆𝑋𝑋Conditional Probability: 𝑃𝑃𝑋𝑋|𝐵𝐵 4 = P[𝑋𝑋 = 4|𝐵𝐵]
= probability that outcome 4 occurs given that B happens
Caution: In this example, 𝐻𝐻 and 𝑁𝑁 are not subsets of 𝑆𝑆𝑋𝑋
Caution: In this example, 𝐵𝐵0 and 𝐵𝐵1 are not subsets of 𝑆𝑆𝑋𝑋
𝑃𝑃𝑋𝑋,𝑌𝑌|𝐵𝐵 𝑥𝑥,𝑦𝑦 : conditional PMF𝑓𝑓𝑋𝑋,𝑌𝑌|𝐵𝐵 𝑥𝑥,𝑦𝑦 : conditional PDF𝐸𝐸[𝑔𝑔(𝑋𝑋,𝑌𝑌)|𝐵𝐵]: conditional expectation
𝐸𝐸 𝐸𝐸 𝑋𝑋 𝑌𝑌 = 𝐸𝐸 𝑔𝑔 𝑌𝑌 = �𝑦𝑦
𝑔𝑔 𝑦𝑦 𝑃𝑃𝑌𝑌(𝑦𝑦)
Optional
About correlation coefficient 𝝆𝝆𝑿𝑿,𝒀𝒀