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.
- It will be graded pass-fail.
- I won't know the grade for 6 months.
- The probability of a pass is under 15%.
- However, a passing grade comes with $150K to do research.
Normal distribution
- Refs (Wikipedia is often excellent, on technical topics)
- They have much more detail than required for this course.
- http://en.wikipedia.org/wiki/Normal_distribution
- http://en.wikipedia.org/wiki/Gaussian_integral - computes the complete integral
- http://en.wikipedia.org/wiki/Multivariate_normal_distribution
- Maple:
with(Statistics); X:=RandomVariable(Normal(0,1)); f:=PDF(X,u); plot(f,u=-2..2); plot(diff(f,u),u=-2..2); F:=CDF(X,u); What is probability that X>1? evalf(subs(u=1,F));
- If mean=500, std=100, prob X>700?
Ex 5.18 p253 jointly Gaussian
- Simple case, {$\rho$} is correlation coefficient.
- Find marginal pdf
5.8 p271 Sum of 2 random variables.
- Sum of 2 indep normal vars.
- Ex 5.40 sum of 2 correlated normal vars.
- Ex 5.41 sum of 2 exponential vars.
5.8.2 p274 Transformations
- CDF of (min,max)