Conditional probability
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This document discusses conditional probability and independence. It defines conditional probability as P(B|A), the probability of event B given that event A has occurred. To calculate this, one considers only the outcomes where A occurred and calculates the fraction where B also occurred. Two events A and B are independent if P(B|A) = P(B), meaning the probability of B is unaffected by the occurrence of A. The general multiplication rule for any events A and B is P(A and B) = P(A) P(B|A) or P(A) P(B|A). Disjoint events cannot be independent as the occurrence of one rules out the other. Conditional probabilities are best understood
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The document discusses measures of central tendency, specifically the mean. It defines the mean as the average of all values in a data set, found by adding all values and dividing by the total number of data points. The mean represents the balance point of a distribution and feels like the center because it is the value where the data balances on either side when represented visually in a histogram. The mean is unique in that a data set only has one mean, and it is influenced by all observations in the data set.Histograms & stem plots
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The document discusses different methods for visualizing data distributions, including histograms and stem-and-leaf displays. It provides examples of histograms of earthquake magnitudes, including a regular histogram showing counts in bins and a relative frequency histogram showing percentages. It also explains that stem-and-leaf displays show the distribution of a quantitative variable while preserving individual values.Recently uploaded (20)
Key Benefits of Implementing Contify's M&CI Platform
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Contify's Market & Competitive Intelligence platform empowers businesses with real-time insights, automated intelligence gathering, and AI-driven analytics. It enhances decision-making, streamlines competitor tracking, and delivers personalized intelligence reports. With Contify, organizations gain a strategic edge by identifying trends, mitigating risks, and seizing growth opportunities in dynamic market landscapes.
For more information please visit here https://www.contify.com/platform/How the Best News APIs Work: A Visual Guide
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Discover how the best news APIs function with this visual guide. Learn how they fetch real-time news, filter content, and integrate seamlessly with apps. Understand key features like authentication, endpoints, and data formats, making it easier to choose the right API for your needs. Perfect for developers and businesses!
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**The Rise and Impact of Large Language Models (LLMs)**
**Introduction**
In the rapidly evolving landscape of artificial intelligence (AI), one of the most groundbreaking advancements has been the development of Large Language Models (LLMs). These AI systems, trained on massive amounts of text data, have demonstrated remarkable capabilities in understanding, generating, and manipulating human language. LLMs have transformed industries, reshaped the way people interact with technology, and raised ethical concerns regarding their usage. This essay delves into the history, development, applications, challenges, and future of LLMs, providing a comprehensive understanding of their significance.
**Historical Background and Development**
The foundation of LLMs is built on decades of research in natural language processing (NLP) and machine learning (ML). Early language models were relatively simple and rule-based, relying on statistical methods to predict word sequences. However, the emergence of deep learning, particularly the introduction of neural networks, revolutionized NLP. The introduction of recurrent neural networks (RNNs) and long short-term memory (LSTM) networks in the late 1990s and early 2000s allowed for better sequential data processing.
The breakthrough moment for LLMs came with the development of Transformer architectures, introduced in the seminal 2017 paper "Attention Is All You Need" by Vaswani et al. The Transformer model enabled more efficient parallel processing and improved context understanding. This led to the creation of models like BERT (Bidirectional Encoder Representations from Transformers) and OpenAIs GPT (Generative Pre-trained Transformer) series, which have since set new benchmarks in AI-driven text generation and comprehension.
**Core Mechanisms of LLMs**
LLMs rely on deep neural networks trained on extensive datasets comprising books, articles, websites, and other textual resources. The training process involves:
1. **Tokenization:** Breaking down text into smaller units (words, subwords, or characters) to be processed by the model.
2. **Pretraining:** The model learns general language patterns through unsupervised learning, predicting missing words or the next sequence in a text.
3. **Fine-tuning:** Adjusting the model for specific tasks, such as summarization, translation, or question-answering, using supervised learning.
4. **Inference:** The trained model generates text based on user input, leveraging probabilistic predictions to produce coherent responses.
Through these mechanisms, LLMs can perform a wide range of linguistic tasks with human-like proficiency.
**Applications of LLMs**
LLMs have found applications across various domains, including but not limited to:
1. **Content Generation:** LLMs assist in writing articles, blogs, poetry, and even code, helping content creators enhance productivity.
2. **Customer Support:** Chatbots and virtual assistants powered by LLMs provide automated yet contPlant Disease Prediction with Image Classification using CNN.pdf
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Plant diseases pose a significant threat to agricultural productivity. Early detection and classification of plant diseases can help mitigate losses. This project focuses on building a Plant Disease Prediction system using Convolutional Neural Networks (CNNs). The system leverages NumPy, TensorFlow, and Streamlit to develop a model and deploy a web-based application. The final model is also containerized using Docker for efficient deployment.
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Updated with the edits we last spoke Bhavana
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en ingles esta prressetnacion es muy buena lasdla lkaskl siempreew aaslkd llasaslas as asasd lk aslk al kjal kj allks
50-Database Efficiency 101 Understanding and Implementing PostgreSQL Indexes....
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Operador de Excel Empresarial - Business Intelligence.Conditional probability
- 1. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario Probability Conditional Probability
- 2. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 2 Conditional Probability When we want the probability of an event from a conditional distribution, we write P(B|A) and pronounce it the probability of B given A. A probability that takes into account a given condition is called a conditional probability.
- 3. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 3 Conditional Probability (cont.) To find the probability of the event B given the event A, we restrict our attention to the outcomes in A. We then find in what fraction of those outcomes B also occurred. Note: P(A) cannot equal 0, since we know that A has occurred. (A and B)( | ) ( ) PP P B A A
- 4. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 4 Independence Independence of two events means that the outcome of one event does not influence the probability of the other. With our new notation for conditional probabilities, we can now formalize this definition: Events A and B are independent whenever P(B|A) = P(B). (Equivalently, events A and B are independent whenever P(A|B) = P(A).)
- 5. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 5 The General Multiplication Rule When two events A and B are independent, we can use the multiplication rule for independent events : P(A and B) = P(A) x P(B) However, when our events are not independent, this earlier multiplication rule does not work. Thus, we need the General Multiplication Rule.
- 6. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 6 The General Multiplication Rule (cont.) We encountered the general multiplication rule in the form of conditional probability. Rearranging the equation in the definition for conditional probability, we get the General Multiplication Rule: For any two events A and B, P(A and B) = P(A) x P(B|A) or P(A and B) = P(B) x P(A|B)
- 7. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 7 Independent Disjoint Disjoint events cannot be independent! Well, why not? Since we know that disjoint events have no outcomes in common, knowing that one occurred means the other didnt. Thus, the probability of the second occurring changed based on our knowledge that the first occurred. It follows, then, that the two events are not independent. A common error is to treat disjoint events as if they were independent, and apply the Multiplication Rule for independent eventsdont make that mistake.
- 8. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 8 Depending on Independence Its much easier to think about independent events than to deal with conditional probabilities. It seems that most peoples natural intuition for probabilities breaks down when it comes to conditional probabilities. Dont fall into this trap: whenever you see probabilities multiplied together, stop and ask whether you think they are really independent.
- 9. Copyright 息 2012 Pearson Canada Inc., Toronto, Ontario 際際滷 15- 9 Tables and Conditional Probability It is easy to understand conditional probabilities with contingency tables