Probability and Statistics for Engineering

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# Probability and Statistics for Engineering - PowerPoint PPT Presentation

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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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 ?

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.

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

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
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

The geometry of randomness

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

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

Law of large numbers or central limit theorem

The previous observation is a special case of the following phenomena:

Regression -- pedestrian detection

Papageorgiou and Poggio, 1998

Experimental Mercedes

A fast version, integrated with a real-time obstacle detection system

MPEG

Constantine Papageorgiou

More regression: talking faces
• Text-to-visual-speech (TTVS) systems:

Movies in faces directory

More regression: talking faces
• Text-to-visual-speech (TTVS) systems:

Movies in faces directory

Descriptive statistics and visualization

Click on mandarin in visual

Click on mandarin in visual

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