NO.PZ2020010304000035
问题如下:
An experiment yields the following data:
It is hypothesized that the data comes from a uniform ditribution, U(0, b).
a. Calculate the sample mean and variance.
b. What are the unbiased estimators of the mean and variance?
c. Calculate the b in U(0, b) using the formula for the mean of a uniform distribution and the value of the unbiased sample mean found in part b.
d. Calculate the b in U(0, b) using the formula for the variance of a uniform distribution and the value of the unbiased sample variance found in part b.
选项:
解释:
a. Use the standard formual to get the sample variance(here, n=15)
b.The sample mean is already unbiased.
For the variance:
c.The mean for a U(a,b) distribution is given as:
μ=(a+b)/2
0.385=(0+b)/2
b=0.77
d. The variance for a U(a,b) distribution is given as:
请问既然题目说是uniform distribution,那a小题中求mean 和variance时,为什么不用uniform distribution中求mean (b+a)/2, 和variance (b-a)^2/12 的公式来求呢