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HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing
Spring 2007
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Harvard-MIT Division of Health Sciences and Technology
HST.582J: Biomedical Signal and Image Processing, Spring 2007
Course Director: Dr. Julie Greenberg
Probability with Venn Diagrams
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams and Probability
Ω
A
B
March 07
HST 582
© John W. Fisher III, 2002-2006
2
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams and Probability
Ω
A
B
March 07
HST 582
© John W. Fisher III, 2002-2006
3
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (Union)
Ω
A∪B
March 07
HST 582
© John W. Fisher III, 2002-2006
4
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (Intersection)
Ω
A∩ B
March 07
HST 582
© John W. Fisher III, 2002-2006
5
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (probability from area)
Ω
A
A∩ B
B
March 07
HST 582
© John W. Fisher III, 2002-2006
6
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (probability relationship)
Ω
A∩ B
March 07
HST 582
© John W. Fisher III, 2002-2006
7
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (combining multiple events)
Ω
A
B
C
March 07
HST 582
© John W. Fisher III, 2002-2006
8
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (combining multiple events)
Ω
A
B
C
March 07
HST 582
© John W. Fisher III, 2002-2006
9
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Venn Diagrams (conditional probabilities)
Ω
A
AB
B
March 07
HST 582
© John W. Fisher III, 2002-2006
10
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Statistical Independence (for events)
Ω
Ω
B
B
AB
A
A
Which Venn diagram depicts independent events?
March 07
HST 582
© John W. Fisher III, 2002-2006
11
Cite as: John Fisher. Course materials for HST.582J / 6.555J / 16.456J, Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].