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Unformatted text preview: 01gxdx For some “complicated” function g. Monte Carlo approach: Make independent draws from a uniform distribution on [0,1] (lots of computer ways to do this.)—let the corresponding random variables ve x 1 ,x 2 , …, then by SLLN: = ( )→ →∞→ 1nk 1ng xi n 01gxdx =expected value of the rv g(x i ) wrt uniform distribution (Nb: {g(x i ): 1<=i<=0} is an iid sequence, (with y i =g(x i )), write common mean ybar= 01gxdx ) Computer’s roles: 1.) Generating random numbers 2.) Computing partial sums, n>infinity Another problem: (actually a special case of integration): compute area or volume of some complicated region D in some “easy” space V. <crash> <see onenote>...
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 Spring '07
 DELCHAMPS
 Algorithms, Probability theory, Stanislaw Ulam

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