lec.02 - ENGG2430C Lecture 2 Probability Model and Axioms...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
ENGG2430C Lecture 2: Probability Model and Axioms Minghua Chen ([email protected]) Information Engineering The Chinese University of Hong Kong Reading: Ch. 1.1 1.2, and 1.3 of the textbook M. Chen ([email protected]) ENGG2430C lecture 2 1 / 23
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Review: Set and Set Operations A set is a collection of objects: S = { x 1 , x 2 ,..., x n } The whole space Ω , and the empty set /0 S c = { x Ω | x / S } S T = { x | x S or x T } S T = { x | x S and x T } M. Chen ([email protected]) ENGG2430C lecture 2 2 / 23
Image of page 2
Review: Venn Diagram (from the textbook) M. Chen ([email protected]) ENGG2430C lecture 2 3 / 23
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Exercise Let A = {set of all persons taller than 1.6 meters}, B = {set of all persons heavier than 60kg}, C = {set of all persons who wear glasses}. Can you relate: (Draw Venn diagrams and also express your mathematics statement in terms of plain English) A B and A B ? ( A B ) c and A c B c ? Answer: ( A B ) c = A c B c If A B , what can you say about the relationship between A c and B c ? What is the corresponding statement in English? I Answer: A c B c . M. Chen ([email protected]) ENGG2430C lecture 2 4 / 23
Image of page 4
Venn Diagrams of De Morgan’s Laws when n=2 ( A S B ) c A c T B c M. Chen ([email protected]) ENGG2430C lecture 2 5 / 23
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
De Morgan’s Laws Two particularly useful properties are given by De Morgan’s laws which state that I ( n S n ) c = T n S c n , I ( T n S n ) c = n S c n Proof of ( n S n ) c T n S c n I Suppose that x ( n S n ) c .Then, x / ∈ ∪ n S n , which implies that for every n , we have x / S n . I Thus, x belongs to the complement of every S n , and x T n S c n . M. Chen ([email protected]) ENGG2430C lecture 2 6 / 23
Image of page 6
Probability Model What is probability model? I A mathematical description of an uncertain situation. Elements of a probability model I The sample space Ω I The probability law (D. P. Bertsekas & J. N. Tsitsiklis, Introduction to Probability, Athena Scientific Publishers, 2002) M. Chen ([email protected]) ENGG2430C lecture 2 7 / 23
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Probability Model: Sample Space A list of all possible outcomes The list must be: I Mutually exclusive
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern