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jojo · 2025年04月21日

计算过程ok,答案差蛮多的 :(

NO.PZ2023091601000049

问题如下:

A quantitative analyst used a simulation to forecast the S&P 500 index value at the end of the year with an index value of 1.800 at the beginning of the year. He generated 200 scenarios and calculated the average index value at year-end to be 1.980, with a 95% confidence interval of (1.940, 2.020). In order to improve the accuracy of the forecast, the quantitative analyst increased the number of scenarios to attain a new 95% confidence interval of (1.970, 1.9901) with the same sample mean and the same sample standard deviation. How many scenarios were used to generate this result?

选项:

A.

400

B.

800

C.

1600

D.

3200

解释:


就是四舍五入也有点勉强!

1 个答案

李坏_品职助教 · 2025年04月22日

嗨,爱思考的PZer你好:


第一次置信区间的下限是1.94,所以μ-2.33*σ/根号n1 = 1.94。 上限是2.02,所以μ+2.33*σ/根号n1 = 2.02,联立方程可求出μ=1.98. 题目说n1 = 200,所以可求出σ=0.243.


第二次置信区间的下限是1.97,所以μ-2.33*σ/根号n2=1.97,所以1.98-2.33*σ/根号n2 = 1.97。

上限是1.9901,所以1.98+2.33*σ/根号n2 = 1.9901.

(σ同样也等于0.243)


1.98-2.33*0.243/根号n2 = 1.97,

1.98+2.33*0.243/根号n2 = 1.9901.

所以n2 = 3142.5,最接近的就是D。


我觉得你这结果已经比较接近了,3166和3200差距不算大的。

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