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Drink H · 2020年01月15日

问一道题：NO.PZ2020010302000009

  1. FRM I
  2. Quantitative

问题如下：

Consider the following data on a discrete random variable X:

a. Calculate the mean and variance of X.

b. Standardize X and check that the mean and variance of X are 0 and 1 respectively.

c. Calculate the skew and kurtosis of X.

选项：

解释：

a. The mean is -0.803 and the variance is 6.762.

b.


c.


Hence, the skew of X is -0.581 and the kurtosis of X is 2.773.

第二部分的后半句，检查均值和方差分别为0，1，这一步如何做？我试着把标准化后的15个值求方差求出来是0.86.

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品职答疑小助手雍 · 2020年01月15日

这其实就是默认是标准化的一部分，标准正态分布的均值为0，标准差为1，那么把参数标准化的过程，也就是把这15个数值计算一下他们分别离均值有多少个标准差。

那1号举例，（-2.456-mean）/标准差=（-2.456+0.803）/2.6= -0.636

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