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claireteng · 2022年06月22日

请问d问如果用线性插值法算50%的概率的点怎么算

NO.PZ2020010302000010

问题如下:

Suppose the return on an asset has the following distribution:

a. Compute the mean, variance, and standard deviation.

b. Verify your result in (a) by computing E[X2]E[X^2] directly and using the alternative expression for the variance.

c. Is this distribution skewed?

d. Does this distribution have excess kurtosis? e. What is the median of this distribution?

解释:

a. The mean is E[X] = Σx Pr(X = x) = 0.25%.

The variance is Var[X]=Σ(xE[X])2Pr(X=x)=0.000555Var[X] = Σ(x - E[X])^2 Pr(X = x) = 0.000555.

The standard deviation is Var[X]=2.355\sqrt {Var[X]} = 2.355%.

b. E[X2]=Σx2Pr(X=x)=.000561E[X^2] = Σx^2 Pr(X = x) = .000561 and so E[X2](E[X])2=0.000561(.0025)2=.000555E[X^2] - (E[X])^2 = 0.000561 - (.0025)^2 = .000555, which is the same.

c. The skewness requires computing

skew(X)=E[XE[X]]3/σ3=E[(Xμσ)3]=Σ(xμσ)3Pr(Xx)skew(X)=E[X-E[X]]^3/{\sigma^3}=E[(\frac{X-\mu}{\sigma})^3]=Σ(\frac{x-\mu}{\sigma})^3Pr(X-x)

Thus the skewness is 0.021, and the distribution has a mild positive skew.

d. The kurtosis requires computing

kurtosis(X)=E[(XE[X])4]σ4=E[(Xμσ)4]=Σ(xμσ)4Pr(Xx)kurtosis(X)=\frac{E[(X-E[X])^4]}{\sigma^4}=E[(\frac{X-\mu}{\sigma})^4]=Σ(\frac{x-\mu}{\sigma})^4Pr(X-x)

Thus the kurtosis is 2.24. The excess kurtosis is then 2.24 - 3 = -0.76. This distribution does not have excess kurtosis.

e. The median is the value where at least 50% probability lies to the left, and at least 50% probability lies to the right. Cumulating the probabilities into a CDF, this occurs at the return value of 0%.

请问d问如果用线性插值法算50%的概率的点怎么算
3 个答案

品职答疑小助手雍 · 2024年01月14日

中位数应该看累计概率,100%的概率中,累计到50%的位置对应的数字才是中位数。不是按数字的个数进行计算的。

品职答疑小助手雍 · 2022年06月22日

如果你觉得老师讲的东西不清楚,可以针对你觉得讲的不清楚的知识点进行提问,也方便我们改进。

最爱吃排骨 · 2024年01月14日

为啥中位数是0不是1。一共10个数,为啥中位数是第五个不是第六个。

品职答疑小助手雍 · 2022年06月22日

同学你好,d问没有需要求中位数的地方,求的是均值,不需要用线性插值法。

我看了你的不少提问,你应该是听了课也认真想学好的,不过需要一些阐发的思维,讲义里写的主要是方便学员记忆理解的点,何老师上课讲的内容其实已经有了一些阐发和补充了,比如你追问那个条件概率和交集并集结合的计算,这个完全是可以根据条件概率和交集并集的知识结合起来,而且课上33-34页例题也讲过如何结合;互斥一定不独立,独立一定不互斥也是可以根据两者定义推算去理解明白的。

做题的过程是对学过的知识点进行结合运用的过程,考试是不会单纯的考概念的,所以听讲的时候基础知识点作为必须掌握的内容(本题峰度计算不需要用中位数,却问线性插值法属于基础知识掌握不牢)当然很重要,不过也需要多注意老师是如何把基础知识点在例题中运用的,这样才能应对考题。

claireteng · 2022年06月22日

我不认为很多东西老师讲的很清楚,我整遍听下来觉得很多东西讲的比较模糊。

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NO.PZ2020010302000010 问题如下 Suppose the return on asset hthe following stribution:Compute the mean, variance, anstanrviation.Verify your result in (computing E[X2]E[X^2]E[X2] rectly anusing the alternative expression for the variance.Is this stribution skewe es this stribution have excess kurtosis? e. Whis the meof this stribution? The meis E[X] = Σx Pr(X = x) = 0.25%.The varianis Var[X]=Σ(x−E[X])2Pr(X=x)=0.000555Var[X] = Σ(x - E[X])^2 Pr(X = x) = 0.000555Var[X]=Σ(x−E[X])2Pr(X=x)=0.000555.The stanrviation is Var[X]=2.355\sqrt {Var[X]} = 2.355%Var[X]​=2.355.E[X2]=Σx2Pr(X=x)=.000561E[X^2] = Σx^2 Pr(X = x) = .000561E[X2]=Σx2Pr(X=x)=.000561 anso E[X2]−(E[X])2=0.000561−(.0025)2=.000555E[X^2] - (E[X])^2 = 0.000561 - (.0025)^2 = .000555E[X2]−(E[X])2=0.000561−(.0025)2=.000555, whiis the same.The skewness requires computingskew(X)=E[X−E[X]]3/σ3=E[(X−μσ)3]=Σ(x−μσ)3Pr(X−x)skew(X)=E[X-E[X]]^3/{\sigma^3}=E[(\frac{X-\mu}{\sigma})^3]=Σ(\frac{x-\mu}{\sigma})^3Pr(X-x)skew(X)=E[X−E[X]]3/σ3=E[(σX−μ​)3]=Σ(σx−μ​)3Pr(X−x)Thus the skewness is 0.021, anthe stribution ha milpositive skew. The kurtosis requires computingkurtosis(X)=E[(X−E[X])4]σ4=E[(X−μσ)4]=Σ(x−μσ)4Pr(X−x)kurtosis(X)=\frac{E[(X-E[X])^4]}{\sigma^4}=E[(\frac{X-\mu}{\sigma})^4]=Σ(\frac{x-\mu}{\sigma})^4Pr(X-x)kurtosis(X)=σ4E[(X−E[X])4]​=E[(σX−μ​)4]=Σ(σx−μ​)4Pr(X−x)Thus the kurtosis is 2.24. The excess kurtosis is then 2.24 - 3 = -0.76. This stribution es not have excess kurtosis.e. The meis the value where least 50% probability lies to the left, anleast 50% probability lies to the right. Cumulating the probabilities into a C, this occurs the return value of 0%. 请问带概率也可以计算机计算吗?如何计算?计算器能否计算kurtosis、skewness

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2024-01-14 11:57 1 · 回答

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2024-01-14 11:54 2 · 回答