![Page 1: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/1.jpg)
Lecture 2: probability concepts II.
![Page 2: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/2.jpg)
Kolmogorov: axioms of probability theory and the Bayesian viewpoint
![Page 3: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/3.jpg)
(Ω, F, P) probability space:
• sample space Ω (set of all possible outcomes)• set of events F • each event is a subset of Ω containing zero or more outcomes• probability measure P: probability of some event A is P(A)
union of mutually exclusive
Kolmogorov probability concept
(satisfied by frequentist definition of probabilities)
disjoint
![Page 4: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/4.jpg)
Kolmogorov probability concept
![Page 5: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/5.jpg)
Kolmogorov probability concept
A or B A and B
http://www.math.uah.edu/stat/
Venn diagrams at web site ofProbability, Mathematical Statistics, Stochastic Processes:
![Page 6: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/6.jpg)
Kolmogorov probability concept
![Page 7: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/7.jpg)
Kolmogorov probability concept
![Page 8: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/8.jpg)
Kolmogorov probability concept
![Page 9: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/9.jpg)
Kolmogorov probability concept
![Page 10: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/10.jpg)
Kolmogorov probability concept
![Page 11: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/11.jpg)
Kolmogorov probability concept
![Page 12: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/12.jpg)
Bayes’ theorem
![Page 13: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/13.jpg)
?
Bayes’ theorem
![Page 14: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/14.jpg)
Bayes’ theorem
![Page 15: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/15.jpg)
Bayes’ theorem
![Page 16: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/16.jpg)
Bayes’ theorem
![Page 17: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/17.jpg)
Bayes’ theorem
![Page 18: Lecture 2: probability concepts II. TTGGG (HI) now have TGGG is still a threat." P(Hi T) so, P (HI T) ... regardless of the order of seeing the data All priors P (Hi) are actually](https://reader030.vdocuments.mx/reader030/viewer/2022021505/5aff3ef77f8b9aa34d9011fb/html5/thumbnails/18.jpg)
Bayes’ theorem