10SimulatingRandomVariables

10SimulatingRandomVariables - Simulating Random Variables...

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Unformatted text preview: Simulating Random Variables Jeffrey B. Burl Click to edit Master subtitle style EE 3180 Probability and 11 Introduction n If we want to simulate a system with random inputs, we will need to generate random variables using the computer. Matlab generates RVs with lots of density functions. But, you may want to generate RVs with density functions not available in EE 3180 Probability and 22 n n Simulating Continuous RVs n Generate a RV with U(0,1). n y = rand; n n Find the RV X = Fx-1 (Y ) Fx ( x)Note =6 Pr( X x) = Pr( Fx-1 (Y ) x) =* Pr(Y Fx ( x)) = Fy ( Fx ( x)) n n But Fy ( y ) = y for 0 y 1 33 EE 3180 Probability and So, our RV has the desired distribution! Simulating Discrete RVs n Generate a RV with U(0,1). n y = rand; X = x1 if 0 y Pr( x1 ) Pr( x1 ) + Pr( x2 ) Pr( x1 ) + Pr( x2 ) + Pr( x3 ) X = x2 if Pr( x1 ) < y n Define: X = x3 if Pr( x1 ) + Pr( x2 ) < y etc. n 44 EE 3180 Probability and From a practical standpoint, must Summary n Methods of generating continuous and discrete RV on a computer were presented. Note that result does not work with Gaussian RVs (inverse of distribution function does not exist in closed form). randn command in Matlab can be used EE 3180 Probability and 55 n n ...
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This note was uploaded on 06/16/2010 for the course EE ee3180 taught by Professor Burl during the Spring '10 term at Michigan Technological University.

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10SimulatingRandomVariables - Simulating Random Variables...

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