统计模拟介绍(7)

Solution:

The positioning of the needle relative to nearby lines can be described with a random vector which has components:

A [0, d )

[0, )

The random vector is uniformly distributed on the region [0,d)×[0, ). Accordingly, it has probability density function 1/d . The probability that the needle will cross one of the lines is given by the integral

p

0

l sin

0

1 d

2l dAd d

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