NO.PZ2023091601000058
问题如下:
A risk manager is examining aHong Kong trader’s profit and loss record for the last week, as shown in thetable below:
The profits andlosses are normally distributed with a mean of 4.5 million HKD and assume thattransaction costs can be ignored. Part of the t-table is provided below:
Accordingto the information provided above, what is the probability that this traderwill record a profit of at least HKD 30 million on the first trading day ofnext week?
选项:
A.
About 15%
B.
About 20%
C.
About 80%
D.
About 85%
解释:
When the populationmean and population variance are not known, the t-statistic can be used toanalyze the distribution of the sample mean.
Sample mean = (10 +80 + 90 - 60 + 30)/5 = 30
Unbiased samplevariance = (1/4)[ (-20)^2 + 50^2 + 60^2 + (-90)^2 + 0^2 ] = 14600/4 = 3650
Unbiased samplestandard deviation = 60.4152
Sample standard error= (sample standard deviation)/√5 = 27.0185
Population mean ofreturn distribution = 4.5 (million HKD)
Therefore thet-statistic = (30 – population mean)/Sample standard error = (30 - 4.5)/27.02 =0.9438.
Because we are usingthe sample mean in the analysis, we must remove 1 degree of freedom beforeconsulting the t-table; therefore 4 degrees of freedom are used. According tothe table, the closest possibility is 0.2 = 20%.
一般关于这类题目下意识以为是假设检验,实际上是检验profit不小于30的概率,进行标准化后查分布表