Machine Learning | total sample | 5mins Getting Started | Commission shall study notes (XVIII)

Populations and Samples

• Overall: study (may be an attribute of the object, or some number of indicators) of all, every member of the population is called individual

  Since each individual occurrence is random, so there is also a corresponding number of indicators with randomness. So that the number of indicators can be seen as a random variable, and therefore the distribution of the random variable is the number of indicators in the distribution of the population.

  The overall nature of these indicators is the nature of collective values. In this way, you can use a general random variables and their probability distributions to describe. So in theory, it can be an overall probability distribution equate.

  In view of this, a symbol or a common random variables that represent the overall distribution function. For example, the overall total or X $F(X)$

• Sampling: To determine the overall distribution of the various features and, according to certain rules extracted from the plurality of individual test population was observed, the extraction process to obtain information about the overall.

  Sample: The extracted portion of the subject

  Sample size: the number of individuals included in the sample

  Sample values: Once a given set of samples taken to give the specific number of n $(X_1,X_2,...,X_n)$ , A sample of observed values referred

• Sampling Method: "simple random sampling"

  Features:

  1. Representative: $X_1,X_2,...,X_n$Each has the same overall distribution of the investigated

  2. Independence: $X_1,X_2,...,X_n$Are independent random variables

• Simple random sample: obtained by a simple random sample

  It can be used n mutually independent random variables with the general iid $X_1,X_2,...,X_n$Show

  If the overall distribution function $F(x)$ , it is simple random sample distribution functions of $