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Probability and Statistics for Engineering

STAT 113. Probability and Statistics for Engineering. Instructor: Sayan Mukherjee TAs: N. Pillai, H. Wang. Perspectives on stats. There are three kinds of lies: lies, damned lies, and statistics . B. Disraeli. What is probability ?.

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Probability and Statistics for Engineering

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  1. STAT 113 Probability and Statistics for Engineering Instructor: Sayan Mukherjee TAs: N. Pillai, H. Wang

  2. Perspectives on stats There are three kinds of lies: lies, damned lies, and statistics. B. Disraeli

  3. What is probability ? Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

  4. What is statistics ? Statistics derives from: Latin -- statisticum collegium ("council of state") Italian -- statista ("statesman" or "politician"). Statistik: German first introduced by Gottfried Achenwall (1749), originally designated the analysis of data about the state, or the "science of state". Acquired the meaning of the collection and classification of data generally in the early 19th century. Statistics as inverse probability -- estimating parameters from experimental data

  5. Well-posed problems Inverse problems are typically ill-posed • A problem is well-posed if its solution • exists • is unique • is stable, eg depends continuously on the data

  6. Class requirements and rules Course webpage

  7. First digits http://en.wikipedia.org/wiki/List_of_world_records Count entries starting with: {1,2,3,4,5,6,7,8,9} Count entries ending with: {1,2,3,4,5,6,7,8,9} Accounting fraud

  8. What’s wrong with the heartland ?

  9. It’s the emptiness

  10. The geometry of randomness Dido’s problem (Isoperimetry) : Among all closed level curves of fixed length, find the one that encloses the largest area.

  11. The geometry of Gaussian random variables A Gaussian distribution:

  12. The geometry of Gaussian random variables A draw of n Gaussian random variables is a point in an n-dimensional space. How far from the origin is this point ? For n large the answer is that with very high probability

  13. Law of large numbers or central limit theorem The previous observation is a special case of the following phenomena:

  14. Regression -- pedestrian detection Papageorgiou and Poggio, 1998

  15. Daimler Chrysler

  16. Experimental Mercedes A fast version, integrated with a real-time obstacle detection system MPEG Constantine Papageorgiou

  17. People classification/detection Stuttgart

  18. More regression: talking faces • Text-to-visual-speech (TTVS) systems: Movies in faces directory

  19. More regression: talking faces • Text-to-visual-speech (TTVS) systems: Movies in faces directory

  20. Descriptive statistics and visualization Click on mandarin in visual Click on mandarin in visual

  21. Conclusion Statistics is about predictive modeling that quantifies uncertainty There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. ---- Donald Rumsfeld

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