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5.  Information Theory: Information theory provides mathematical tools for data analysis.
                 6.   Logic and Set Theory: Logic and set theory are used in concepts like expert systems, database systems,
                    and knowledge graphs. Mathematics and AI are deeply integrated fields, with mathematics providing the
                    theoretical foundation for many AI algorithms and techniques.
                 7.   Algorithm design: The design of the algorithms often uses mathematical principles and structures such as
                    functions, matrices and graphs.


                         Statistics


                 Statistics is used for collecting, exploring, and analysing the data. It also helps in concluding data. It enables AI
                 systems to detect patterns, identify relationships, and infer conclusions from data.
                    • Data is collected from various sources.
                    • Data is explored and cleaned to be used.
                    • The analysis of data is done to understand it better.
                    • Conclusions and decisions can be made from the data.
                 Let’s consider an example to illustrate these steps:
                 A school wants to improve the performance of its students and decides to collect data on study habits and
                 grades.
                 •  Collecting Data:  The school conducts a survey where students report the number of hours they
                   study each week and their grades in various subjects.

                                •   Exploring and Cleaning Data: The school first looks at the data to find patterns, like the range
                                  of study hours and grades.
                                  They also clean the data by fixing any missing or incorrect information (e.g., if some students
                                  didn’t fill in all the fields or gave unrealistic answers).
                 •  Analysing Data: The school summarises the average study hours and grades to get an overview.

                   They also check if there is a significant relationship between study hours and grades.

                                •   Drawing Conclusions: The analysis might reveal that students who study for more hours tend
                                  to have higher grades. Based on this conclusion, the school might decide to implement study
                                  support programs to encourage students to study more.


                 Thus, we can say statistics helps in transforming the raw data into meaningful insights, enabling better decisions
                 and strategies in various fields such as business, healthcare, education, and more.



                            a  Brainy Fact


                        As  per  the  statistics,  Netflix  makes  $1  billion  annually  from  automated  personalised
                        recommendations.





                         Application of Statistics


                 Statistics can be used in numerous fields because of its ability to extract meaningful insights from data and assist
                 in decision-making. Let us discuss some of the fields where statistics is used.

                                                                           Maths for AI (Statistics & Probability)   301
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