Expected value of mathematics

One of the most basic mathematical characteristics of random variables. It reflects the average value of random variables. Also called expected value or average value. It is a generalization of simple arithmetic average. For example, if a city has 654.38+million families, 1 000 families have no children, 90,000 families have one child, 6,000 families have two children and 3,000 families have three children, then the number of children in any family in this city is a random variable, which can be taken as 0,654,38+0. The probability of taking 1 is 0.9, that of taking 2 is 0.06, and that of taking 3 is 0.03. Its mathematical expectation is 0× 0.01+/kloc-0 /× 0.9+2× 0.06+3× 0.03, which is equal to 1. 1658.

Definition of mathematical expectation

Definition 1:

According to the definition, the sum of the products of all possible values of a discrete random variable and the corresponding probability p (if there are two dragons) is called mathematical expectation and recorded as fu. If a random variable only gets a limited number of values: x,,, and.

Originated from: research on optimal design and risk decision of retaining wall-also on the Yellow River ... South-to-North Water Transfer Project and water conservancy technology, 2004, Li.

Abstract: Retaining wall, as a retaining structure in general civil engineering, is often used in the transition section between dam wing wall, aqueduct and inverted siphon, and its optimal design is often ignored. In fact, the technical and economic benefits of various retaining walls vary greatly. However, the actual conditions of some projects make some commonly used retaining walls present many limitations. The retaining wall construction of concrete production system in Huangbizhuang Reservoir reinforcement project has taken a step forward in optimization design and achieved remarkable technical and economic benefits. Its experience can be used as reference for similar projects.

Definition 2:

1 The conventional safety factor is selected according to experience, that is, the ratio of the average value of material strength limit (called mathematical expectation in probability theory) to the average value of working stress (mathematical expectation).