Expected value of mathematics
In probability theory and mathematical statistics, mathematical expectation (or simply mean, or expectation) is the sum of the possible results multiplied by the results in each experiment, which is one of the most basic mathematical characteristics. It reflects the average value of random variables.
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.
For a better understanding, please refer to the extended materials.
Both discrete random variables and continuous random variables are determined by the range of random variables.
Variables can only take discrete natural numbers, that is, discrete random variables. For example, if you toss 20 coins at a time, K coins face up, and K is a random variable. The value of k can only be a natural number 0, 1, 2, …, 20, but not a decimal 3.5 or an irrational number.
K is a discrete random variable.
If a variable can take any real number in an interval, that is, the value of the variable can be continuous, this random variable is called continuous random variable. For example, the bus runs every 15 minutes, and the waiting time of people on the platform is a random variable. The value range of X is [0, 15], which is an interval. Theoretically, this interval can take any real number 3.5 or irrational number.
And so on, so this random variable is called continuous random variable.