我本来的意思没说清，被昏昏一逼就乱说，固然是功力不行，也因为看到北大的就心慌意乱，可能是从前落下的病根。
现在从头说，过去的都不算。
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。随意就要问，为什么会这样呢？
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。
关于最大熵分布，依赖于给定的限制。From wiki:
Given mean and standard deviation: the normal distributionThe 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 distributionThe 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.