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？
