正态分布推导汇编.docx
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正态分布的概率密度函数的推导
An interesting question was posed in a Statistics assignment which was to show that the
standard normal distribution was valid - ie the integral from negative infinity to infinity
equated to one and in doing so showed the derivation of the part of the normal pdf
.
A friend of mine and I decided to try to derive the normal pdf and the thinking went along the
lines of the central limit theorem which states that the mean of any probability distribution
becomes normal as the number of trials increases.
The derivation of this is well known.but we asked ourselves how the normal distribution was
first achieved. There is another 'normal' derivation which is the binomial approximation and
it is through this direction that we wondered how to derive the normal distribution from the
binomial as n gets large.
So the general approach we will take is to take a binomial distribution, then increase the
number of samples n.
(提出一个有趣的问题是在统计分配，这是表明，标准正态分布是有效的 - 即从负无穷到正无穷的积分等
。
我，我的一个朋友决定尝试推导出正常的 PDF 和沿中心极限定理指出，任何概率分布的均值作为试验增加
这个推导是众所周知的。 但我们问自己如何正态分布首次实现。 有另一种“正常”的推导，这是二项式近似
和它是通过这个方向，我们想知道如何从二项式正态分布为 n 变大。
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