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梦梦 · 2024年11月09日

两个问题

NO.PZ2023091601000058

问题如下:

A risk manager is examining a Hong Kong trader’s profit and loss record for the last week, as shown in the table below:

The profits and losses are normally distributed with a mean of 4.5 million HKD and assume that transaction costs can be ignored. Part of the t-table is provided below:

According to the information provided above, what is the probability that this trader will record a profit of at least HKD 30 million on the first trading day of next week?

选项:

A.

About 15%

B.

About 20%

C.

About 80%

D.

About 85%

解释:

When the population mean and population variance are not known, the t-statistic can be used to analyze the distribution of the sample mean.

Sample mean = (10 + 80 + 90 - 60 + 30)/5 = 30

Unbiased sample variance = (1/4)[ (-20)^2 + 50^2 + 60^2 + (-90)^2 + 0^2 ] = 14600/4 = 3650

Unbiased sample standard deviation = 60.4152

Sample standard error = (sample standard deviation)/√5 = 27.0185

Population mean of return distribution = 4.5 (million HKD)

Therefore the t-statistic = (30 – population mean)/Sample standard error = (30 - 4.5)/27.02 = 0.9438.

Because we are using the sample mean in the analysis, we must remove 1 degree of freedom before consulting the t-table; therefore 4 degrees of freedom are used. According to the table, the closest possibility is 0.2 = 20%.

1、这道题就是求P(X=30million)吧?而不是P(X大于等于30million)?

2、为什么30减去的是总体均值,而不是样本均值?


2 个答案
已采纳答案

pzqa39 · 2024年11月11日

嗨,努力学习的PZer你好:


检验统计量的公式为:样本均值-hypothesized value。这道题hypothesized value就是总体均值,因为我们假设检验的目的是确认样本均值与总体均值之间的差异是否显著,总不能用样本均值-样本均值吧,这不是自己减自己么?上下统一是说分子用样本均值-hypothesized value,分母也用样本均值。

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梦梦 · 2024年11月12日

哦哦,明白了,谢谢

pzqa39 · 2024年11月10日

嗨,爱思考的PZer你好:


1、不是,题目中所求的是“至少 HKD 30 million”,所以是≥30,而不是=30


2、因为我们在进行的是一个假设检验,目的是确定样本中的观察值(即 30 million)与已知的总体均值之间的差异是否显著。在这道题目中,总体均值为 4.5 million(即我们认为总体的平均收益是 4.5 million)。我们要评估的是:样本中的一个观察值(30 million)是否显著高于这个总体均值。


如果我们用样本均值(30 million)来计算,那就相当于在比较样本本身,这不会告诉我们样本与总体的关系。

我们的目的是验证样本观察值(30 million)是否与总体均值(4.5 million)有显著差异,减去总体均值表示的是:样本均值偏离总体均值的程度,即我们要验证样本的结果与总体预期是否存在显著性差异。

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梦梦 · 2024年11月10日

课上不是讲过上下要统一吗?分子减去的是总体方差,周一到周五可以计算出总体方差,也可以计算出(n-1)的样本方差,来决定标准误,但分母却是又选择的样本方差除以根号5,这不是不统一了?

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2024-11-02 11:20 1 · 回答

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