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Many things in physics require the mathematical use of probability. One area for which our understanding is based on pure probability is radioactive decay.
许多物理现象需要概率论的数学工具。其中，放射性衰变的理解完全基于概率论。
Although one cannot be sure about the outcome of a single event when it depends upon probability, the calculation of the probability of a specific outcome is a precise mathematical process. For independent events, the probability is described by the binomial distribution.
尽管当事件依赖于概率时，无法确定单个事件的结果，但计算特定结果的概率是一个精确的数学过程。对于独立事件，概率由二项分布描述。
For physical applications, the binomial distribution is often inconvenient because it contains the factorials which are hard to manage when the number of events is large. From the behavior of gas molecules to the processes of radioactive decay or nuclear scattering, the numbers are very large indeed. Two approaches to probability can be used in place of the binomial distribution in physical settings. When the number is very large, then the binomial distribution can be approximated by a Gaussian distribution. In other physical cases where the probability for a given event is very small, the distribution can be approximated by a Poisson distribution.
对于物理应用来说，二项分布往往不太方便，因为它包含阶乘项，当事件数量很大时难以处理。从气体分子的行为到放射性衰变或核散射的过程，数字确实非常大。在物理情境中，可以采用两种概率方法来代替二项分布。当数量非常大时，二项分布可以近似为高斯分布。在其他物理情况下，当某个事件的概率非常小时，分布可以近似为泊松分布。
In dealing with molecular distributions, the Maxwell speed distribution is an important element. Kinetic theory also gives us a development of the mean free path of molecules. Together they can give us a means for calculating the frequency of molecular collisions.
在处理分子分布时，麦克斯韦速率分布是一个重要因素。气体动理论也给出了分子平均自由程的进一步发展。两者结合可以为我们计算分子碰撞频率提供一种方法。
Another application of molecular distributions is the Barometric formula, which allows us to predict the change in atmospheric pressure with height.
分子分布的另一个应用是巴氏公式，它允许我们预测大气压随高度的变化。
Homework set #2
第二套作业
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