人的身高分布服从近似正态分布是从很多统计数据看出来的.所以就要问，为什么会这样呢？

引用：

It [clt] explains why many human characteristics follow the normal curve, as attributes such as height or weight can be thought of as a sort of “average”. If we think of human weight or height as being a “sort of mean” of many factors (such as heredity, diet, race, sex, many others) then the Central Limit Theorem would lead us to expect that such human characteristics will follow the normal distribution.

这就是说正态分布显示影响身高的独立而差不多重要的因素很多，没有主因可集中研究用以帮助预测一个个体的未来身高。在此意义上说预测难，或预测的研究难，因为无主因可抓。假若是[a,b]上的均匀分布，则研究一个人的身高就很有可能发现影响所有人身高的共同原因。

如果随机变量们不是相加而是相乘，且相乘的随机变量个数也是随机的并服从几何分布，则乘积服从幂律。对沙堆来说，一粒沙的随机滑动引起随机个沙粒的滑动，并继续如此，历一个几何分布的次数后停止，所以沙堆的坍塌服从幂律。这说明同等重要的随机因素，即各沙粒的随机位置，太多，且无主因可抓住研究。推之以说明地震，可猜测地震区有很多碎块或将碎的块，一但动起来就以乘的方式扩张，而导致幂律，无主因可抓住研究。所以预测的研究难，因为不知道研究什么好。如果震频对震强是均匀分布，则一个地震的原因可能是所有地震的共因，政府可抓住一个地震集中投资研究。

关于最大熵分布，依赖于给定的限制。From wiki:

Given mean and standard deviation: the normal distribution

The normal distribution N(μ,σ2) has maximum entropy among all real-valued distributions with specified mean μ and standard deviation σ. Therefore, if all you know about a distribution is its mean and standard deviation, it is often reasonable to assume that the distribution is normal.

Uniform and piecewise uniform distributions

The uniform distribution on the interval [a,b] is the maximum entropy distribution among all continuous distributions which are supported in the interval [a, b] (which means that the probability density is 0 outside of the interval).

The uniform distribution on the finite set {x1,...,xn} (which assigns a probability of 1/n to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set.

Positive and given mean: the exponential distribution

The exponential distribution with mean 1/λ is the maximum entropy distribution among all continuous distributions supported in [0,∞) that have a mean of 1/λ.

In physics, this occurs when gravity acts on a gas that is kept at constant pressure and temperature: if X describes the height of a molecule, then the variable X is exponentially distributed (which also means that the density of the gas depends on height proportional to the exponential distribution). The reason: X is clearly positive and its mean, which corresponds to the average potential energy, is fixed. Over time, the system will attain its maximum entropy configuration, according to the second law of thermodynamics.