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ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute

Lecture 1

  1. Why probability is useful
    1. AT&T installed bandwidth to provide level of iphone service (not all users want to use it simultaneously).
    2. also web servers, roads, cashiers, ...
    3. fair price for financial CDO that reduces risk
  2. Model
    1. Real thing too expensive, dangerous, time-consuming (aircraft design).
    2. Capture the relevant, ignore the rest.
    3. Coin flip: relevant: it's fair? not relevant: copper, tin, zinc, ...
    4. Validate model if possible.
  3. Computer simulation model
    1. For systems to complicated for a simple math equation (i.e., most systems outside school)
    2. Often a graph of components linked together, e.g., with
      1. Matlab Simulink
      2. PSPICE
    3. many examples, e.g. antilock brake, US economy
    4. Can do experiments on it.
  4. Deterministic model
    1. Resister: V=IR
    2. Limitations: perhaps not if I=1000000 amps. Why?
    3. Limitations: perhaps not if I=0.00000000001 amps. Why?
  5. Probability model
    1. Roulette wheel: {$p_i=\frac{1}{38} $} (ignoring http://www.amazon.com/Eudaemonic-Pie-Thomas-Bass/dp/0595142362 )