Monte Carlo Integration

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Monte Carlo Integration
A method using simulation to find the area
(volume) of a region (space).
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X N(100, 225)
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XUniform(112,126) YUniform(0,0.02) If (x,y) is
beneath the curve then the event is satisfied,
otherwise, it is not. Probability (area) is the
proportion of time the event is satisfied times
the area being sampled.
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Let S of times (x,y) is in the blue region, n
of iterations in simulation A area of
sampling region (126 112)(0.02 0) 0.28 p
proportion of sampling region that satisfies the
event S Bin(n, p)
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Estimate the volume of the sphere centered at
(5,-3,8) with radius 4.
Note V (4/3)pr3 268.0826
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X Uniform(1, 9) Y Uniform(-7, 1) Z
Uniform(4, 12)
Volume of sampling region (9 1)(1 (7))(12
4) 512
If
then the sampled point is inside the sphere.
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S of points sampled inside sphere n of
iterations in simulation VRegion volume of
sampling region VSphere volume to be estimated
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