Trying to Ace Class 9 Math and AI (unit-4) for High Score?
Well, here it is! These Math and AI Notes of Class 9 AI cover all important topics in a simplified manner to support smart revision and effective exam preparation.

Importance of Math for AI

How are Math and AI Related?

• Math is the Study of Patterns.
• Patterns are arrangements or sequences that follow a rule.
• For example:
  • Number patterns: 2, 4, 6, 8, …
  • Image patterns: shapes repeating in order
  • Language patterns: common sentence structures
• Humans use patterns to solve puzzles and understand the world around them.

AI is a Way to Recognize Patterns

• Artificial Intelligence learns patterns from data just like humans learn from experience.
• AI can see patterns in different types of data – numbers, images, and speech and text. 
• These patterns help AI make decisions such as:
  • Identifying objects in images
  • Predicting weather
  • Recommending videos
  • Translating languages

Hence,
▪ Mathematics is the study of patterns and relationships.
▪ Artificial Intelligence (AI) recognizes patterns in data to make decisions.
▪ Therefore, AI uses Mathematics to understand patterns, learn from data, and make intelligent decisions.

Essential Mathematics for AI

AI uses different branches of Mathematics to solve problems.

1. Statistics – Exploring Data

• Statistics helps AI understand and analyze data such as:
  • Finding the middle value
  • Finding the most common value
  • Understanding trends
  • Example: In given sequence – 11, 22, 33, 44, 55
    Middle value = 33

2. Calculus – Training and Improving AI

• Calculus helps AI measure changes and improve accuracy such as:
  • Which line is more slanted?
  • Which shape has more area?
• The idea of slope is important in AI learning.

3. Linear Algebra – Finding Unknown Values

• Linear Algebra helps AI work with large amounts of data and relationships such as:
  • A has 2 plants
  • B has 3 plants
  • C has 1 plant
  • D has 7 plants
  • Total plants: 2+3+1+7 = 13
• AI uses similar calculations to count, organize, and process information.

4. Probability – Predicting Events

• Probability helps AI predict what might happen such as:
  • Coin toss result
  • Weather prediction
  • Recommendation systems
• For a coin toss – Possible outcomes = Head or Tail
  P(Head) = 1/2.P(Tail) = 1/2

Statistics

Statistics is the branch of Mathematics used for collecting, organizing, exploring, analyzing, and interpreting data in order to draw conclusions and make decisions.

Steps Involved in Statistics

1. Data Collection

Information is collected from different sources such as surveys, observations, measurements, or records.

2. Data Organization and Exploration

The collected data is arranged, cleaned, and examined so that it can be used properly.

3. Data Analysis

The data is analysed to identify patterns, trends, and useful information.

4. Drawing Conclusions

Based on the analysis, decisions and predictions can be made.

Applications of Statistics

Statistics is used in many real-life situations.

1. Sports

• Statistics helps in:
  • Predicting the performance of sports teams
  • Comparing player performance
  • Planning game strategies
• Example: Statistics were used during the Tokyo 2020 Olympics to study the spread of COVID-19 and make safety decisions.

2. Disaster Management

• Authorities use statistics to:
  • Predict natural disasters
  • Alert people living in dangerous areas
  • Estimate population and resources needed in affected regions
• Examples:
  • Flood prediction
  • Earthquake risk analysis
  • Cyclone warnings

3. Disease Prediction

• Governments and hospitals use statistics to:
  • Identify diseases affecting people the most
  • Track the spread of diseases
  • Improve vaccination drives
• Example: During COVID-19, statistics helped identify areas with rising infection cases.

4. Weather Forecasting

• Computers use statistical data from previous years to forecast weather conditions such as:
  • Rainfall
  • Temperature
  • Storms
  • Climate changes

Probability and Its Role in AI

Introduction to Probability

Probability is a branch of Mathematics that helps us measure the chance of an event happening. It tells us how likely or unlikely something is to occur.

For example, when a coin is tossed, there are two possible outcomes:
Head (H)
Tail (T)
Both outcomes have an equal chance of occurring.

Probability Formula

The probability of an event is calculated using the following formula:
P(E) = Number of Favorable Outcomes / Total Number of Possible Outcomes
For a coin toss:
P(Head) = 1/2.P(Tail) = 1/2
This means the chance of getting a Head or Tail is equal.

Types of Probability Events

1. Certain Event: An event that will definitely happen. Example – The sun will rise tomorrow.
Probability = 1

2. Likely Event: An event that has a high chance of happening. Example: Carrying an umbrella during heavy clouds may mean rain is likely.

3. Unlikely Event: An event that has a low chance of happening. Example: Getting full marks without studying is unlikely.

4. Impossible Event: An event that cannot happen. Example: Picking a red ball from a bag containing only blue balls.
Probability = 0

5. Equal Probability Event: When all outcomes have the same chance of occurring. Example: Tossing a fair coin

The probability of any event always lies between 0 and 1.
0<=P(E)<=1

Applications of Probability

Probability is widely used in everyday life to predict events and make better decisions. Some important applications of probability are:

1. Sports

• Probability is used in sports to estimate the performance of players and teams.
  • In cricket, probability can help estimate a batsman’s batting average.
  • Batting average represents the number of runs a batsman is likely to score before getting out.
  • For example: if a batsman scored 45 runs out of 100 through boundaries in the previous match, there is a possibility that around 45% of his runs in the next match may also come from boundaries.

2. Weather Forecasting

• One of the most common applications of probability is weather forecasting.
  • Weather forecasters use probability to predict the chances of rain, snow, storms, clouds, and other weather conditions.
  • Predictions are made by analyzing past and present weather data.
  • For example: a forecast may say, “There is a 70% chance of rain today between 4 PM and 6 PM.”

3. Traffic Estimation

• Probability is also used to estimate traffic conditions.
• People often predict traffic based on:
  • Time of day
  • Weather conditions
  • Location
  • Previous traffic patterns
• For example: if there is a 90% probability of heavy traffic between 6 PM and 7:30 PM, people may choose to travel later.
  P(Heavy Traffic) = 0.9