08SimHw3sol_supplementary

08SimHw3sol_supplementary - → E h X for n → ∞(1 The...

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IEOR 4404 Assignment #3 Solutions Supplementary Simulation September 26, 2008 Prof. Mariana Olvera-Cravioto Page 1 Assignment #3 Solutions Supplementary 1. If you use MATLAB, there are build-in functions in MATLAB that can generate random variable. Examples are available online. Uniformly distributed www.mathworks.com/access/helpdesk/help/techdoc/ref/rand.html Binomial random www.mathworks.com/access/helpdesk/help/toolbox/stats/binornd.html Normally distributed www.mathworks.com/access/helpdesk/help/toolbox/stats/normrnd.html For other well-know distributions in simulation, you can google them, like ”help matlab exponential random”. 2. In Problems 2 and 3 and 4, we need the theorem below. 1 n n X i =1 h ( X i ) a.s.
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Unformatted text preview: → E ( h ( X )) for n → ∞ (1) The evidence can be found at wiki. http://en.wikipedia.org/wiki/SLLN (click # 2.2 The strong law) For example, if you can prove 2 Z-2 e x + x 2 dx = 1 Z e (4 u-2)+(4 u-2) 2 4 du = E [4 e (4 U-2)+(4 U-2) 2 ] Then you might define some h such that E ( h ( U )) = E (4 e (4 U-2)+(4 U-2) 2 ) and apply (1), estimating E ( h ( U )) by simulating 1 n n X i =1 h ( U i ) We prefer uniformly distributed random variable on [0,1] in the algorithm, as it is fast and straightforward to simulate. 3. About the change of variables, some examples can be found online. http://en.wikipedia.org/wiki/Change of variables (click # 2 Examples)...
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