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What are the expectation and variance of binomial distribution?
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.

Variance is a measure of dispersion when probability theory and statistical variance measure random variables or a set of data. Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value). The variance (sample variance) in statistics is the average value of the square of the difference between each sample value and the average value of all sample values. In many practical problems, it is of great significance to study variance or deviation.

Extended data

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 natural number 0, 1, 2, …, 20, and cannot be decimal number 3.5 and irrational number √20, so 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, any real number 3.5, irrational number √20, etc. Can be taken in this interval, so this random variable is called continuous random variable.

Baidu Encyclopedia-Mathematical Expectation

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