Is the mathematical expectation E X of the random variable X an average? What kind of average is it?

The sum of the product of all possible values xi and the corresponding probability pi(=xi) of a discrete random variable is called the mathematical expectation of the discrete random variable. It's the concept.

The random variable x is discrete, and if there are n possible values of x, then e(x) = sum (xn n) = sum (xn) n = x can be taken as the average of all values (note: because x is random, the probability of each of his possible values being selected is the same and is 1 n, xn is only one of x all possible values).

Continuity: If the distribution function f(x) of the random variable x can be expressed as the integral of a non-negative integrable function f(x), then x is called a continuous random variable, and f(x) is called the probability density function of x (distribution density function).

e(x)=integral(xf(x) dx) from a to b, where f(x) is a probability distribution function, and since it is continuous, f(x) is 1 (b-a).

rs, for reference only.

Actually, it means average.

In discrete quantities, it is the average.

In a continuous random variable, it is the average of the area.

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e(x) is a real number, not a variable, it is a weighted average, which is different from the general average, which essentially reflects the true average of the possible values of the random variable x, also known as the mean.

Mathematical expectation is a term for arithmetic averages, which is to find the evenly distributed expectation (a+b) 2 by definition, and the expectation of a general continuous function is found by definition.

In probability theory and statistics, mathematical expectation (mean) (or mean, also known as expectation) is the sum of the probabilities of each possible outcome in an experiment multiplied by its outcome, and is one of the most basic mathematical characteristics. It reflects the magnitude of the average value of the random variable.

It's important to note that expected value is not necessarily the same as "expectation" in common sense – "expected value" may not be equal to every outcome. The expected value is the average of the output values of that variable. Expected values are not necessarily included in the set of output values of variables.

If the random variable x is mathematically expected, then e(e(ex)ex) ex is a constant.

set, ex=c

then, d(ex)=d(c)=0

e[d(ex)]=e(0)=0

It's important to note that expected value is not necessarily the same as "expectation" in common sense – "expected value" may not be equal to every outcome. The expected value is the average of the output values of that variable. Expected values are not necessarily included in the set of output values of variables.

If the random variable x is mathematically expected, then e(e(ex)<>

In probability theory and statistics, mathematical expectation (mean) is the sum of the probabilities of each possible outcome in an experiment multiplied by its outcome, and is one of the most basic mathematical characteristics. It reflects the magnitude of the average value of the random variable.

It's important to note that expected value is not necessarily the same as "expectation" in common sense – "expected value" may not be equal to every outcome. The expected value is the average of the output values of that variable. Expected values are not necessarily included in the set of output values of variables.

Summary. A random variable represents a real-value function (all possible sample points) of various outcomes in a random phenomenon (a phenomenon that does not always have the same result under certain conditions). For example, the number of passengers waiting at a bus stop at a given time, the number of calls received by the exchange station in a certain time, etc., are all examples of random variables.

The essential difference between the uncertainty of random variables and fuzzy variables is that the results of the latter are still uncertain, i.e., fuzzy. Random events, whether they are directly related to quantity or not, can be quantified, that is, they can be expressed in a quantitative way. The advantage of quantifying random events is that random phenomena can be studied by means of mathematical analysis.

With regard to the random variable x, where e(x) and e(x) are appropriate squares of .

Hello, I am inquiring for you here, please wait a while, I will reply to you immediately Hello, I am happy to answer for you. The value in the example is 3 to 8

x is a random variable, x 2 is also a random variable, e(x) is the average of this discrete variable, and e(x 2) is the average of x 2. For example: 1,2,3,4,5 average is:

3, while the average of 1,4,9,16 is. They are also related, d(x)=e(x2)-e(x)2

A random variable represents a real-value function (all possible sample points) of various outcomes in a random phenomenon (a phenomenon that does not always have the same result under certain conditions). For example, the number of passengers waiting at a bus stop at a given time, the number of calls received by the exchange station in a certain time, etc., are all examples of random variables. The essential difference between the uncertainty of random variables and fuzzy variables is that the results of the latter are still uncertain, i.e., fuzzy.

Random events, whether they are directly related to quantity or not, can be quantified, that is, they can be expressed in a quantitative way. The advantage of quantifying random events is that random phenomena can be studied by means of mathematical analysis.

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e(x) is already a number, and its expectation is still its own e(x).

e(x^2)-2ex+1=10

e(x^2)-4ex+4=6

So ex=7 e(x 2)=16d(x)=e(x)-[e(x)] 2 =16-(7 2) 2