MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 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].