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

Lecture 19

What profs do outside class (not part of this course)

Last week I wrote a proposal (like a big term paper) on this topic: Water Sustainability and Climate.

  1. It will be graded pass-fail.
  2. I won't know the grade for 6 months.
  3. The probability of a pass is under 15%.
  4. However, a passing grade comes with $150K to do research.

Normal distribution

  1. Refs (Wikipedia is often excellent, on technical topics)
    1. They have much more detail than required for this course.
    2. http://en.wikipedia.org/wiki/Normal_distribution
    3. http://en.wikipedia.org/wiki/Gaussian_integral - computes the complete integral
    4. http://en.wikipedia.org/wiki/Multivariate_normal_distribution
  2. Maple:
    with(Statistics);
    X:=RandomVariable(Normal(0,1));
    f:=PDF(X,u);
    plot(f,u=-2..2);
    plot(diff(f,u),u=-2..2);
    F:=CDF(X,u);
    What is probability that X>1?  
    evalf(subs(u=1,F));
If mean=500, std=100, prob X>700?

Ex 5.18 p253 jointly Gaussian

  1. Simple case, {$\rho$} is correlation coefficient.
  2. Find marginal pdf

5.8 p271 Sum of 2 random variables.

  1. Sum of 2 indep normal vars.
  2. Ex 5.40 sum of 2 correlated normal vars.
  3. Ex 5.41 sum of 2 exponential vars.

5.8.2 p274 Transformations

  1. CDF of (min,max)