Topic According to the observed suspicious behaviors and related data of criminal suspects in a community within t time, the possible criminal patterns of criminal suspects are given, which requires us to establish a mathematical model to solve the following three problems after observing three sets of data:

(1), according to the data in annex 1, find out the possible perpetrators and crime patterns, and judge the correct rate of the results;

(2) After using floating-point numbers to improve the statistical method, according to the data in Annex 2, find out several possible different crime patterns and their implementers, and judge their correct rate;

(3) In view of the fact that the criminal suspect will change his criminal pattern once according to the change of the situation, it is required to determine the time when the criminal suspect changed his criminal pattern according to the data in Annex 3, and to find out the date of change, different criminal patterns and criminals.

2 problem analysis

3 Model Assumption and Symbolic Description

3. 1 model hypothesis

3. The observation data of suspicious behavior given in1.1is objective and true;

3. 1.2 The case can only be caused by some or all of these suspects.

3. 1.3 Assume that the dates with the same data represent the same crime pattern;

3.2 Symbolic description

4 model establishment and solution

4. 1 conditional quantization processing

Definition of crime rate

4. 1. 1 Let the total number of observation days be m, the number of criminal suspects be n, and the number of suspicious abnormal behaviors of I criminal suspects be. Then, if the number of abnormal behaviors at the time of the crime is, let the suspicious crime rate be the probability that a criminal suspect can be suspected, and the suspicious rate of I criminal suspects can be expressed as, which can indicate the suspicion of I criminal suspects.

If the abnormal rate is defined as (), the abnormal rate of the ith criminal suspect is ().

If the crime rate is defined as (), the crime rate of the I-th suspect is ()

The difference between the abnormal rate of the crime recorded as the I-th suspect and its abnormal rate.

Let the crime rate of the I-th suspect be, then (that is, the suspicious rate MINUS the crime rate, which mainly describes the possibility of crime)