The so-called confidence, also called reliability, or confidence level, confidence coefficient, refers to the degree of confidence of a particular individual in the authenticity of a particular proposition, that is, probability is a measure of the rationality of an individual's belief.
Confidence level refers to the probability that the overall parameter value falls within a certain area of the sample statistical value; Confidence interval refers to the error range between the statistical value of the sample and the overall parameter value at a certain confidence level.
The greater the confidence interval, the higher the confidence level.
It is said that the value should be checked backwards. Given that a = 0,05, the solution is as follows:
Calculate a/2 = 0,025.
Calculate1-0,025 = 0,975.
Take out the standard normal distribution table, check the intermediate probability value and find 0,975. At this time, the vertical and horizontal corresponding values are 1, 9 and 0,6 respectively, that is, z (1, 96) = 0,975.
So u0,025 =1,96.
Normal distribution, also known as Gaussian distribution, is a very important probability distribution in the fields of mathematics, physics and engineering, and has great influence in many aspects of statistics. If the random variable obeys the position parameter and the scale parameter is a probability distribution, it is recorded as follows: its probability density function is a normal distribution, and the mathematical expected value or expected value is equal to the position parameter, which determines the position of the distribution; The square root or standard deviation of its variance is equal to the proportional parameter, which determines the size of the distribution. The probability density function curve of normal distribution is bell-shaped, so people often call it bell-shaped curve. What we usually call the standard normal distribution is the normal distribution of position parameters and scale parameters (see the green curve on the right).
The density function of normal distribution is characterized by: with respect to μ symmetry, it reaches the maximum at μ, takes a value of 0 at positive (negative) infinity, and has an inflection point at μ σ. Its shape is high in the middle and low on both sides, and the image is a bell curve above the X axis. When μ = 0 and σ 2 = 1, it is called standard normal distribution, and it is recorded as n (0, 1).
When a μ-dimensional random vector has similar probability laws, it is said that this random vector follows a multidimensional normal distribution. Multivariate normal distribution has good properties, such as the edge distribution of multivariate normal distribution is still normal distribution, and the random vector obtained by arbitrary linear transformation is still multidimensional normal distribution, especially its linear combination is unary normal distribution.