MITESD_70Jf09_lec03

# MITESD_70Jf09_lec03 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu ESD.70J / 1.145J Engineering Economy Module Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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ESD.70J Engineering Economy Module - Session 3 1 ESD.70J Engineering Economy Fall 2009 Session Three Michel-Alexandre Cardin Prof. Richard de Neufville
ESD.70J Engineering Economy Module - Session 3 2 Question from Session Two Yesterday we used uniformly distributed random variables to model uncertain demand This implies identical probability of median as well as extreme high and low outcomes. This is may not be appropriate… What alternative probability distributions should we use to sample demand?

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ESD.70J Engineering Economy Module - Session 3 3 Session three Modeling Uncertainty • Objectives: – Generate random numbers from various distributions (Normal, Lognormal, etc) • So you can incorporate in your model as you wish – Generate and understand random variables that evolve through time (stochastic processes) • Geometric Brownian Motion, Mean Reversion, S- curve
ESD.70J Engineering Economy Module - Session 3 4 Open ESD70session3-1Part1.xls (Two parts because RAND() calls and graphs take long to compute and update for every Data Table iteration…) About random number generation

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ESD.70J Engineering Economy Module - Session 3 5 About random number generation • Generate normally distributed random numbers: – Use NORMINV(RAND(), μ , σ ) (NORMINV stands for “the inverse of the normal cumulative distribution”) μ is the mean σ is the standard deviation • In cell B1 in “Sim” sheet, type in “=NORMINV(RAND(), 5, 1)” • Create the Data Table for 2,000 samples • Press “command =“ or “F9”, see what happens
ESD.70J Engineering Economy Module - Session 3 6 Random numbers from triangular distribution • Triangular distribution could work as an approximation of other distribution (e.g. normal, Weibull, and Beta) – Faster computationally • Try “=RAND()+RAND()” in the Data Table output formula cell B1 • Press “command =“ or “F9”, see what happens

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ESD.70J Engineering Economy Module - Session 3 7 Random numbers from lognormal distribution • A random variable X has a lognormal distribution if its natural logarithm has a normal distribution • Using LOGINV(RAND(), ln_ μ , ln_ σ ) –ln_ μ is the mean of ln(X) σ is the standard deviation of ln(X) • In the Data Table output formula cell B1, type “=LOGINV(RAND(), 2, 0.3)” • Press “command =“ or “F9”, see what happens
ESD.70J Engineering Economy Module - Session 3 8 Give it a try! Check with your neighbors… Check the solution sheet… Ask me questions…

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ESD.70J Engineering Economy Module - Session 3 9 • We have just described the probability density function (PDF) of random variable x, or f(x) • We can now study the time function of
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## This note was uploaded on 12/04/2011 for the course ESD 15.094 taught by Professor Jiesun during the Spring '04 term at MIT.

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MITESD_70Jf09_lec03 - MIT OpenCourseWare http:/ocw.mit.edu...

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