Daily article 72: Understand Normal distribution by common sense
Unlike discrete random variables, continuous random variables have infinite outcomes, so the probability of any specific outcome is 0. Therefore, we don’t care about the probability of a specific outcome for continuous random variables. Rather, we are curious about the probability that the outcome falls within a specific interval, which contains infinite outcomes as well. A frequency distribution demonstrates how the outcomes are distributed.
Normal distribution is also called Gaussian distribution to commemorate the contribution made by the great mathematician, Gaussian. Remember the famous Gaussian Algorithm from middle school? That’s him. Normal distribution is very important in statistics because many statistical results follow the normal distribution. Normal distribution is a symmetric distribution that can be described solely by two parameters: mean μ and standard deviation σ (middle school math again). Mean determines the normal distribution’s middle line and standard deviation determines the level of dispersion. Let’s take a look at the graph below:
The normal distribution is a bell-shape distribution, which means the probabilities of intervals near to mean are greater than that of intervals far away from mean. The result coordinates with our common sense. For example, there are more people of average height and few people are extremely tall or short. We can find random variables of normal distribution in many areas in our daily life，among which the equity return is the most common one in financial world. It’s also pretty straightforward: we have higher chances to get a return around expected return, and lower chances to get extremely large gains or losses.
每日文章（七十二） 用常识来理解正态分布
与离散随机变量不同，连续随机变量有无数种结果，所以任一特定结果的可能性，无限接近于0。因此，我们并不关心连续随机变量的某一结果的概率，我们希望了解的是结果落入某一区间的概率（这一区间也包含无数个可能结果）。频率分布描述了这些结果是怎样分布的。
正态分布也叫做高斯分布，目的是纪念伟大的数学家高斯在研究正态分布中做出的贡献。还记得我们在初中学习的高斯算法（首项加末项乘以项数除以2）吗？就是这个高斯。在统计学中，正态分布非常重要，很多统计结果都是正态分布的。正态分布图是一个轴对称的分布图，它由两个参数确定：均值和标准差（仍然是初中数学知识）。均值确定了正态分布的中线在哪，标准差确定了正态分布的离散程度。让我们看看下面的正态分布图：
正态分布是一个钟的形状，这意味著相对于远离均值的区间，该连续变量的结果有更大概率落入接近均值的区间，这其实和我们的常识是一致的。举例来说，大部分人的身高接近于平均身高，只有少数人特别高或者特别矮。事实上，符合正态分布的变量在生活中广泛存在，其中金融领域最常见的就是股票的回报率。这也很容易理解：我们有更高的概率取得一个接近期望收益率的收益率，而大赚或者大亏的概率则比较低。
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