Sample mean and sample variance are two very important statistics in mathematical statistics. According to general textbooks, if the population obeys normal distribution, the sample mean and sample variance are independent of each other. ?

Extended data:

Characteristics of sample mean:

1, the sampling distribution of sample mean is the distribution formed by all sample mean, that is, the probability distribution of μ. The sampling distribution of sample mean is symmetrical in shape;

2. With the increase of sample size n, whether the original population obeys normal distribution or not, the sampling distribution of sample mean will tend to normal distribution, and the mathematical expectation of its distribution is the population mean μ and the variance is 1/n of population variance, which is the central limit theorem;

3. Let the population * * * have n elements, and randomly select a sample with n capacity. When resetting sampling, * * * has n different sampling methods, that is, n different samples can be formed. Without repeated sampling, * * * has n possible samples;

4. Each sample can calculate a mean value, and the distribution formed by all possible sampling mean values is the distribution of sample mean values. But in reality, it is impossible to extract all samples, so the probability distribution of sample mean is actually a theoretical distribution.

Baidu Encyclopedia-Simple Random Sampling