Open Bo The second chapter still reviews the most basic concepts of statistics involved in data analysis, including the following concepts:Expectation, variance, standard deviation, deviation, residuals, covariance.0 Discrete random variables, continuous random variables random variables (variable) represent real-valued single-valued functions that randomly experiment with various results. For example, the number of passengers waiting at a bus stop at a certain time, and the points each time the dice are thrown, are examples of random variables.
A randomized trial may result (known as a basic event) of the entire composition of a basic space Ω. The random variable x is a function that defines the value of the base space Ω as a real number, that is, every point in the basic space Ω, that is, each basic event has a point on the real axis corresponding to it. For example, if you throw a dice, all of its possible results are 1, 2, 3, 4, 5, and 6, and if you define x as the number of points that appear when you throw a dice, x is a random variable and x is 1,2,3,4,5,6 when the 1,2,3,4,5,6 point appears.
discrete random variables: Random variables are discrete and can only take discrete and finite values. For example, throw a dice, can only take 1,2,3,4,5,6, such as 6 natural numbers, it is not possible to take 3.5 of the value of this number; a person's age, can only take 0~150岁 between the values; The number of cars produced by a car factory in one year can only range from 0 to a certain number of natural numbers. Continuous random variables: If a random variable can take any real number in a certain interval, and there are more or fewer real numbers in that interval, then the value of the variable is continuous, called the continuity random variable. For example, to count the height of a piece of wheat in a Tanaka, the height range can be taken from [20,100]cm, where the height of wheat growth is available; statistics of the height of a man over 18 years of age range from [100,240]cm, to every real number within this range, Also known as continuous random variables.
1 Expectations The expectation of discrete stochastic variables is discussed first. In probability theory and statistics, the expectation of a discrete random variable (expectation, symbol e) is the sum of the probabilities of each possible result in the experiment multiplied by the result value. if it is assumed that the probability of the outcome of each test is equal, the expectation is that the random test repeats multiple results at the same opportunity, and calculates the average of the equal probability "expectation". It is important to note that the expected value may not be equal to each result, because the expectation is the average of the output values of the variable, and the expected value is not necessarily contained in the variable's output values collection. the formulation of a discrete random variable expectation is expressed as follows, suppose that the random variable is \ (x\), value \ ({x}_{i} (i = 1, 2, ..., n) \), corresponding to the occurrence probability \ ({p}_{i} (i = 1, 2, ..., n) \), \ (E (X) \) as expected of the random variable :
\ (E (X) = \sum_{i=1}^{n}{p}_{i}{x}_{i}\)
When \ ({p}_{i} (i = 1, 2, ..., n) \) equals, also \ ({p}_{i}=\frac{1}{n}\), \ (E (X) \) can be simplified to:\ (E (X) = \frac{1}{n}\sum_{i=1}^{n}{x}_{i}\) the expectation of a continuous random variable can be obtained by using the integral of finding the value of a random variable and the corresponding probability product, and setting \ (x\) is a continuous random variable, and \ (f (x) \) is the corresponding probability density function, then the desired \ (E (x) \) is:\ (E (x) = \int XF (x) dx\)2 VarianceIn probability and mathematical statistics, the variance (Variance, symbol D) is used to measure the degree of deviation between a random variable and its mathematical expectation (that is, the mean), in which the variance is the average of the sum of squares of the difference between each data and its average value. Variance is a criterion for measuring the degree of dispersion of data, which indicates the degree of deviation between the data and the data Center (mean), and the greater the variance, the greater the extent of the data being diverted from the center. The discrete random variable is still taken as an example, assuming that the random variable is \ (x\), the value \ ({x}_{i} (i = 1, 2, ..., n) \), \ (\mu\) is the mathematical expectation (mean) of the random variable, then the variance of the discrete random variable \ (x\) can be expressed as:\ (D (X) = \frac{1}{n}\sum_{i=1}^{n}{({x}_{i}-\MU)}^{2}\)
Expectation, variance, standard deviation, standard error, deviation, residuals, covariance
