Mathematical expectation is a statistic, which represents the average value of random variables, while the population parameter is a constant describing the characteristics of the population.

In some cases, especially when the probability distribution function is uniform or normal, the mathematical expectation may be equal to the overall parameters. For example, the random variable X obeys the normal distribution, and its expected value (mathematical expectation) is equal to the mean value of the distribution, which is also one of the overall parameters to describe the normal distribution.

However, for general random variables and distributions, there is not necessarily a direct and equal relationship between mathematical expectations and overall parameters. The population parameter is usually a fixed value describing the nature of the population, while the mathematical expectation is based on the statistics of the sample, which will change with the change of the sample.

The relationship between overall parameters and mathematical expectations depends on specific probability distribution and statistical properties, and cannot be generalized.

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In probability theory and statistics, mathematical expectation (or expectation value) is a concept that represents the average value of random variables. It is the weighted average of all possible values, and the weight is the probability of each value.

For the discrete random variable x, the mathematical expectation E(X) is calculated as follows:

[E(X)=\sum{i}xiP(X=x_i)]

Where (xi) is the possible value of a random variable and (P(X=xi)) is the probability of taking the value of (x_i).

For continuous random variable x, the mathematical expectation E(X) is calculated as follows:

[e(x)=\int_{-\infty}^{\inftyxf(x)dx]

Where (f(x)) is the probability density function of x.

Mathematical expectation can be understood as the average of a random variable in a large number of repeated experiments. It is an important concept and widely used, such as in statistics, economics, engineering and other fields.

It should be noted that the expected value is not necessarily equal to the common sense "expectation"-"expected value" is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.