Math for AI - Unit 2 PDF

DELHI PUBLIC SCHOOL BANGALORE EAST ARTIFICIAL INTELLIGENCE UNIT – 2 :: MATH FOR AI Importance of Math for AI How are Math and AI related? Math is the study of patterns ▪ To solve the puzzles, you identify an order/arrangement...

DELHI PUBLIC SCHOOL BANGALORE EAST ARTIFICIAL INTELLIGENCE UNIT – 2 :: MATH FOR AI Importance of Math for AI How are Math and AI related? Math is the study of patterns ▪ To solve the puzzles, you identify an order/arrangement in the list of numbers or the images. ▪ This arrangement is called a pattern. ▪ These patterns exist all around us. ▪ We have patterns in numbers, images, and language. AI is a way to recognize patterns ▪ AI can learn to recognize patterns, like human beings. ▪ AI can see patterns in different types of data - numbers, images, and speech andtext. ▪ These patterns help AI to solve puzzles – like identifying dogs and muffins, or predicting hurricanes! Hence, ▪ Math is the study of patterns ▪ AI is a way to recognize patterns in order to take decisions ▪ AI needs Math to study and recognize patterns in order to take decisions Can you identify any pattern in the image given below? Understanding math will help us to better understand AI and its way of working, but what kind of math is needed for AI? Essential Mathematics for AI ▪ 11, 22, 33, 44, 55 – Can you find out the middle value from the given numbers? ▪ In the given figure, which of the two lines is more slanted? Line 1 or Line 2? ▪ A has 2 plants, B has 3 plants, C has 1 plant, D has 7 plants. How many plants are there in total? Just like us, AI can also solve 4 type of problems using Math. AI uses Math for: ▪ Statistics (Exploring data): Example – What is the middle value of the data? Which is the most common value in the data? ▪ Calculus (training and improving AI model): Example – which line is more slanted? Which figure covers more area? ▪ Linear Algebra (finding out unknown or missing values): Example – How many plants are therein total? How many cars are there in a city? ▪ Probability (predicting different events): Example – what will be the possible results of a coin toss? Will it rain tomorrow? Statistics Definition of Statistics:” Statistics is used for collecting, exploring, and analyzing the data. It also helps in drawing conclusions from data.” ▪ Data is collected from various sources. ▪ Data is explored and cleaned to be used. ▪ Analysis of data is done to understand it better. ▪ Conclusions and decisions can be made from the data. Applications of Statistics: ▪ Predict the performance of sports teams ▪ It can be used to find out specific things such as: o the reading level of students o the opinions of voters o the average weight of a city’s resident Some more applications of Statistics :: Disaster Management Authorities use statistics to alert the citizens residing in places that might be affected by a natural disaster in near future. The disaster management teams use statistics to know about the population, and about the services and infrastructure present in the affected area. Sports The Tokyo 2020 Olympics were postponed due to the developing global situation in light of the Covid-19 pandemic. Statistics revealed that COVID cases sharply increased in Japan during the planned period of Olympics.  Disease prediction ▪ US government uses statistics to understand which disease is affecting the population the most. ▪ This helps them in curing these diseases more effectively. ▪ Example - government can analyze the areas where COVID cases are increasing, or where the vaccination drive needs to be improved. Weather forecast ▪ ▪ Computers use statistics to forecast weather. ▪ They compare the weather conditions with the information about past seasons and conditions. Few more facts Kids watch around 1.5-3 hours of TV per day while being in childcare. 72% of teens often (or sometimes) check for messages or notifications as soon as they wake up, while roughly four-in-ten feel anxious when they do not have their cellphone with them. 77% of children don’t get enough physical exercise. Almost a quarter (23%) of children aged five to 16 believe that playing a computer game with friends is a form of exercise. 69% of all children experience one or more sleep-related problems at least a few nights a week. Only 54% of US children aged 3 to 5 years attend full-day preschool programs. At least 264 million children worldwide (about 12%) don’t go to school. 3.2 Probability Purpose: To understand the possibility of occurrence of an event. Introduction to probability Probability is a way to tell us how likely something is to happen. For example – When a coin is tossed, there are two possible results or outcomes: heads (H) or tails (T) The probability equation defines the likelihood of the happening of an event. It is the ratio of favorableoutcomes to the total favorable outcomes. The probability formula can be expressed as, Probability of an Event = Number of Favorable Outcomes / Total Number of Possible Outcomes We say that the probability of the coin landing H is ½ and the probability of the coin landing T is ½ When we talk about probability, we use a few terms that help us understand the chances for something to happen. Probability can be expressed in the following ways: ▪ Certain events: An event will happen without a doubt ▪ Likely events: The probability of one event is higher than the probability of another event ▪ Unlikely events: One event is less likely to happen than another event ▪ Impossible events: There's no chance of an event happening ▪ Equal Probability events: Chances of each event happening is same The probability of an event occurring is somewhere between impossible and certain. If an event is certain or sure to happen, it will have a probability of 1. For example, the probability that it will rain in the state of Florida at least once in a specific year is 1. If an event will never happen or is impossible, it will have a probability of 0. For example, the probability that you can pick a red ball from a bag containing only blue balls is 0. Let’s try to understand the concept of Probability using a relatable example. You want to go to your best friend's birthday party next Saturday. Your parents decide to make a deal with you. Scenario 1 Scenario 4 Probability – Applications Sports ▪ Probability can be used in estimating batting average in Cricket. ▪ Batting average in Cricket represents how many runs a batsman would score before getting out. ▪ For instance, if a batsman had scored 45 runs out of 100 from only boundaries in the last match. Then, there is a chance that he will score 45% of his runs in the next match from boundaries. Weather Forecasting ▪ One of the most common real-life examples of usingprobability is weather forecasting. ▪ It is used by weather forecasters to assess how likely it is that there will be rain, snow, clouds, etc., on a givenday in a certain area. ▪ Forecasters may say things like “there is a 70% chance of rain today between 4 PM and 6 PM” to indicate a medium to high likelihood of rain during certain hours. Traffic Estimation ▪ Regular people often use probability when they decide to drive to someplace. ▪ Based on the time of day, location in the city, weather conditions, etc. people tend to make probability predictions about how bad traffic will be during a certain time. ▪ For example, if you think there’s a 90% probability that traffic will be heavy from 6 PM to 7:30 PM in your vicinity then you may decide to wait during that time.  DELHI PUBLIC SCHOOL BANGALORE EAST ARTIFICIAL INTELLIGENCE UNIT 3: MATH FOR AI 1. If you are to throw an arrow to this pie chart, in which color is the arrow more likely to fall? a) Red b) Blue c) Yellow d) Green 2. If you select a balloon without looking, how likely is it that you will pick a blue one? a) Probable b) Certain c) Unlikely d) Impossible 3. With one throw of a 6-sided die, what's the probability of getting an even number? a) 1/5 b) 2/5 c) 5/6 d) 1/2 4. Which of the following is an equation? a) 2x + 5 b) x + 2 = 4x c) x^2 + 2x d) 5 + 5x + 5x^2 5. What is the value of x? 10x-8=6x a) 8 b) 4 c) 2 d) 6 6. Which two are examples of descriptive statistics? a) Median and correlation. b) Mean and standard deviation. c) Mode and regression analysis. d) Variance and Hypothesis testing. 7. What is the probability of getting head when you toss a coin once? a) 0.75 b) 1 c) 0 d) 0.5 8. Getting seven in die throwing is a possible event. (True/False). 9. The median of the data: 155, 160, 145, 149, 150, 147, 152, 144, 148 is a) 149 b)150 c)147 d)144 Answer the following question: 1. Explain the relationship between Mathematics and Artificial Intelligence, providing justification for their interconnection. Mathematics and artificial intelligence (AI) are closely related. AI uses mathematical concepts such as linear algebra, calculus, probability theory, and statistics to understand and imitate human behavior. Additionally, AI can help explore and understand mathematical concepts in fields like computer vision and deep learning. On the other hand, mathematics can also benefit from AI by using machine learning to search for patterns and relations between mathematical objects. 2. Aman is confused, how probability theory is utilized in artificial intelligence, help Aman by providing two examples to illustrate its importance. Probability theory is used in artificial intelligence (AI) to model uncertainty, quantify risk, and make informed decisions. Probability theory is a cornerstone for building reliable, adaptable, and interpretable AI systems. ▪ Probability is used to classify an email as spam or not, a probabilistic model can estimate the probability of spam based on the email content, sender, and other features. ▪ An AI system that was trained in the past on historical weather data in your location might, therefore, consider seasonal trends when calculating the probability of rain. 3. Define Certain events and likely events with examples. In probability, a certain event is an event that is guaranteed to happen, while a likely event is an event that will probably occur: Certain event :An event that is sure to occur, with a probability of 1. For example, rolling a dice and getting a number less than seven is a specific event. Likely event :An event that will probably occur, with a probability close to 1. For example, tossing one hundred coins and getting at least one head, or rolling two die and getting a sum greater than or equal to three. 4. Write any two examples of Impossible and equal probability events. Impossible Event: An event that will surely not occur at any experiment is known as an impossible event. Examples: (i) Getting Seven in die throwing. (ii) Getting a ‘Sum of 13 while throwing a pair of dice. Equal probability Event: When there is no other go expect the occurrence of one event in preference to the other. This is known as equally likely events. Example: When an unbiased coin is tossed the chances of getting ahead or a tail are the same.