M 1.5 p4.q
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A die is tossed and reported to have landed on six. The chance that it actually landed on six is 1/6, as there is a 1 in 6 chance of any single number being rolled on a standard six-sided die.
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1. Bayes' theorem is used to calculate unknown probabilities based on additional information provided by experiments or past records. It involves calculating inverse or posterior probabilities.
2. The theorem states that the probability of an event occurring given some evidence is equal to the probability of the evidence given the event occurred, multiplied by the original probability of the event, divided by the total probability of the evidence.
3. Bayes' theorem is widely used in business and engineering to help decision makers account for uncertainty in their analyses and decisions. It allows probabilities to be updated as new information becomes available.M 1.5 p4.s
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A die is tossed and reported as a six. The chance the report is truthful is calculated using Bayes' theorem. The probability the die actually landed on six, given the report, is 1/6, as the report has a 1/6 chance of being truthful for each possible outcome of the die toss.M 1.5 p3.s
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An urn contains 4 balls that are drawn randomly. Two balls drawn were found to be white. The probability that all balls are white is calculated using Bayes' rule. Let W be the event that all balls are white and D be the event that two white balls were drawn. Bayes' rule is used to calculate P(W|D) = P(D|W)P(W) / P(D).M 1.5 p3.q
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The probability that all the balls are white given that two balls drawn were white depends on the total number of balls and the number of white balls drawn. With an urn containing 4 balls total and 2 white balls drawn randomly, there is a 1/6 probability that all the balls are white.M 1.5 p2.s
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A class has students who are very intelligent, medium, or below average. The probabilities of failing a viva voce exam are 0.1, 0.3, and 0.5 respectively for each group. Using Bayes' rule, the probability a student who passed the exam is below average can be calculated by dividing the probability of being below average and passing by the total probability of passing.M 1.5 p2.q
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In a class, 20% of students were very intelligent, 60% were medium, and 20% were below average. The probability of a very intelligent student failing their viva voce exam is 0.1, a medium student failing is 0.3, and a below average student failing is 0.6. If a student passed the exam, the probability they are below average is 0.2/0.7 = 20/70 = 1/3.M 1.5 p1.s
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Plant I manufactures p% of scooters and Plant II manufactures q% of scooters. p% of scooters from Plant I meet the standard quality, and q% of scooters from Plant II meet the standard quality. To calculate the probability that a standard quality scooter came from Plant I, use Bayes' rule and the given probabilities to get p/(p+q). Similarly, the probability that a standard quality scooter came from Plant II is q/(p+q).M 1.5 p1.q
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A company has two plants that manufacture scooters. Plant I produces 50% of scooters and Plant II produces the other 50%. Plant I produces 70% standard quality or better scooters, while Plant II only produces 30% standard quality or better. If a scooter is known to be standard quality, there is a 70% chance it came from Plant I and a 30% chance it came from Plant II.M 1.4 rm
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This document discusses theorems in probability and their proofs. It begins by stating that theorems help evaluate probabilities of compound events simply. Several probability theorems and their proofs are then presented, including:
1) The probability of an impossible event is zero.
2) The probability of a complementary event A' is 1 - P(A).
3) For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B).
4) If A and B are independent, P(A and B) = P(A)P(B).
Examples are provided to demonstrate applying the theorems to probability problems involving events described usingM 1.4 ap1
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This document contains 15 probability exercises involving events such as drawing cards from a deck, outcomes of experiments, tickets in an urn, applications to jobs, components of equipment, throws of a die, and groups of children. The exercises cover concepts like mutually exclusive and independent events, and calculating probabilities using given individual probabilities or odds.M 1.3 rm
M 1.3 rmRamakrishna Paduchuri
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There are four main definitions of probability:
1. Mathematical (or classical) definition which assumes outcomes are equally likely and calculates probability as number of favorable outcomes over total outcomes. It breaks down if outcomes are not equally likely or the sample space is infinite.
2. Statistical (or empirical) definition which calculates probability as the limiting ratio of number of times an event occurs over number of trials as trials approach infinity. It may not have a unique limit.
3. Subjective definition where probabilities are assigned based on experience and belief and can vary between people.
4. Axiomatic definition which defines probability as a measure satisfying three axioms: non-negativity, normality, and countable additivityM 1.1 rm
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1. The document discusses concepts from probability including sets, elements, unions, intersections, complements, permutations, combinations, and distributions. It provides examples and formulas for calculating things like the number of possible outcomes of events.
2. Key concepts covered include defining sets and their operations, the difference between permutations and combinations, and formulas for counting the number of ways to arrange or select objects with or without repetition.
3. Examples show how to use formulas to calculate things like the number of possible hands that could be dealt from a deck of cards or words that can be formed from letters in a given word.M 1.3 ap1
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1. The document defines probability and provides examples of calculating probabilities for events like throwing dice, drawing balls from bags, and random arrangements of letters or numbers. It includes 29 practice problems calculating probabilities for scenarios involving dice, cards, balls in bags, randomly selecting numbers, and randomly arranging letters.
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M 1.5 rm
M 1.5 rmRamakrishna Paduchuri
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1. Bayes' theorem is used to calculate unknown probabilities based on additional information provided by experiments or past records. It involves calculating inverse or posterior probabilities.
2. The theorem states that the probability of an event occurring given some evidence is equal to the probability of the evidence given the event occurred, multiplied by the original probability of the event, divided by the total probability of the evidence.
3. Bayes' theorem is widely used in business and engineering to help decision makers account for uncertainty in their analyses and decisions. It allows probabilities to be updated as new information becomes available.M 1.5 p4.s
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A die is tossed and reported as a six. The chance the report is truthful is calculated using Bayes' theorem. The probability the die actually landed on six, given the report, is 1/6, as the report has a 1/6 chance of being truthful for each possible outcome of the die toss.M 1.5 p3.s
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An urn contains 4 balls that are drawn randomly. Two balls drawn were found to be white. The probability that all balls are white is calculated using Bayes' rule. Let W be the event that all balls are white and D be the event that two white balls were drawn. Bayes' rule is used to calculate P(W|D) = P(D|W)P(W) / P(D).M 1.5 p3.q
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The probability that all the balls are white given that two balls drawn were white depends on the total number of balls and the number of white balls drawn. With an urn containing 4 balls total and 2 white balls drawn randomly, there is a 1/6 probability that all the balls are white.M 1.5 p2.s
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In a class, 20% of students were very intelligent, 60% were medium, and 20% were below average. The probability of a very intelligent student failing their viva voce exam is 0.1, a medium student failing is 0.3, and a below average student failing is 0.6. If a student passed the exam, the probability they are below average is 0.2/0.7 = 20/70 = 1/3.M 1.5 p1.s
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Plant I manufactures p% of scooters and Plant II manufactures q% of scooters. p% of scooters from Plant I meet the standard quality, and q% of scooters from Plant II meet the standard quality. To calculate the probability that a standard quality scooter came from Plant I, use Bayes' rule and the given probabilities to get p/(p+q). Similarly, the probability that a standard quality scooter came from Plant II is q/(p+q).M 1.5 p1.q
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A company has two plants that manufacture scooters. Plant I produces 50% of scooters and Plant II produces the other 50%. Plant I produces 70% standard quality or better scooters, while Plant II only produces 30% standard quality or better. If a scooter is known to be standard quality, there is a 70% chance it came from Plant I and a 30% chance it came from Plant II.M 1.4 rm
M 1.4 rmRamakrishna Paduchuri
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This document discusses theorems in probability and their proofs. It begins by stating that theorems help evaluate probabilities of compound events simply. Several probability theorems and their proofs are then presented, including:
1) The probability of an impossible event is zero.
2) The probability of a complementary event A' is 1 - P(A).
3) For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B).
4) If A and B are independent, P(A and B) = P(A)P(B).
Examples are provided to demonstrate applying the theorems to probability problems involving events described usingM 1.4 ap1
M 1.4 ap1Ramakrishna Paduchuri
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This document contains 15 probability exercises involving events such as drawing cards from a deck, outcomes of experiments, tickets in an urn, applications to jobs, components of equipment, throws of a die, and groups of children. The exercises cover concepts like mutually exclusive and independent events, and calculating probabilities using given individual probabilities or odds.M 1.3 rm
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There are four main definitions of probability:
1. Mathematical (or classical) definition which assumes outcomes are equally likely and calculates probability as number of favorable outcomes over total outcomes. It breaks down if outcomes are not equally likely or the sample space is infinite.
2. Statistical (or empirical) definition which calculates probability as the limiting ratio of number of times an event occurs over number of trials as trials approach infinity. It may not have a unique limit.
3. Subjective definition where probabilities are assigned based on experience and belief and can vary between people.
4. Axiomatic definition which defines probability as a measure satisfying three axioms: non-negativity, normality, and countable additivityM 1.1 rm
M 1.1 rmRamakrishna Paduchuri
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1. The document discusses concepts from probability including sets, elements, unions, intersections, complements, permutations, combinations, and distributions. It provides examples and formulas for calculating things like the number of possible outcomes of events.
2. Key concepts covered include defining sets and their operations, the difference between permutations and combinations, and formulas for counting the number of ways to arrange or select objects with or without repetition.
3. Examples show how to use formulas to calculate things like the number of possible hands that could be dealt from a deck of cards or words that can be formed from letters in a given word.M 1.3 ap1
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1. The document defines probability and provides examples of calculating probabilities for events like throwing dice, drawing balls from bags, and random arrangements of letters or numbers. It includes 29 practice problems calculating probabilities for scenarios involving dice, cards, balls in bags, randomly selecting numbers, and randomly arranging letters.
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3. Answers to each probability question are not provided, as the purpose of the document appears to be providing probability practice problems rather than solutions.Ma2002 1.23 rm
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2. It shows that the error of the finite difference solution converges to zero as the grid size decreases, establishing convergence of the method.
3. It analyzes the stability of explicit finite difference schemes for a test differential equation. The type of difference approximation used for the first derivative term depends on the sign of a constant, in order to satisfy the stability condition for the scheme.Ma2002 1.22 rm
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￥ Factors Affecting Viscosity: Temperature, composition, flow rate.
Clinical Relevance: Impact of blood viscosity in cardiovascular health.
Fluid Dynamics: Laminar vs. turbulent flow, Reynolds number.
Extension Techniques:
Chromatography (adsorption, partition, TLC, etc.)
Electrophoresis (protein/DNA separation)
Sedimentation and Centrifugation methods.spinal cord disorders (Myelopathies and radiculoapthies)
spinal cord disorders (Myelopathies and radiculoapthies)Mohamed Rizk Khodair
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Myelopathies
Radiculopathies 
Drive Supporter Growth from Awareness to Advocacy with TechSoup Marketing Ser...
Drive Supporter Growth from Awareness to Advocacy with TechSoup Marketing Ser...TechSoup
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Learn how to understand and optimize your audience experience with awareness of your impact.
Ancient Stone Sculptures of India: As a Source of Indian History
Ancient Stone Sculptures of India: As a Source of Indian HistoryVirag Sontakke
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This Presentation is prepared for Graduate Students. A presentation that provides basic information about the topic. Students should seek further information from the recommended books and articles. This presentation is only for students and purely for academic purposes. I took/copied the pictures/maps included in the presentation are from the internet. The presenter is thankful to them and herewith courtesy is given to all. This presentation is only for academic purposes.YSPH VMOC Special Report - Measles Outbreak Southwest US 5-3-2025.pptx
YSPH VMOC Special Report - Measles Outbreak Southwest US 5-3-2025.pptxYale School of Public Health - The Virtual Medical Operations Center (VMOC)
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A measles outbreak originating in West Texas has been linked to confirmed cases in New Mexico, with additional cases reported in Oklahoma and Kansas. The current case count is 817 from Texas, New Mexico, Oklahoma, and Kansas. 97 individuals have required hospitalization, and 3 deaths, 2 children in Texas and one adult in New Mexico. These fatalities mark the first measles-related deaths in the United States since 2015 and the first pediatric measles death since 2003.
The YSPH Virtual Medical Operations Center Briefs (VMOC) were created as a service-learning project by faculty and graduate students at the Yale School of Public Health in response to the 2010 Haiti Earthquake. Each year, the VMOC Briefs are produced by students enrolled in Environmental Health Science Course 581 - Public Health Emergencies: Disaster Planning and Response. These briefs compile diverse information sources including status reports, maps, news articles, and web content into a single, easily digestible document that can be widely shared and used interactively. Key features of this report include:
- Comprehensive Overview: Provides situation updates, maps, relevant news, and web resources.
- Accessibility: Designed for easy reading, wide distribution, and interactive use.
- Collaboration: The unlocked" format enables other responders to share, copy, and adapt seamlessly. The students learn by doing, quickly discovering how and where to find critical information and presenting it in an easily understood manner.
CURRENT CASE COUNT: 817 (As of 05/3/2025)
Texas: 688 (+20)(62% of these cases are in Gaines County).
New Mexico: 67 (+1 )(92.4% of the cases are from Eddy County)
Oklahoma: 16 (+1)
Kansas: 46 (32% of the cases are from Gray County)
HOSPITALIZATIONS: 97 (+2)
Texas: 89 (+2) - This is 13.02% of all TX cases.
New Mexico: 7 - This is 10.6% of all NM cases.
Kansas: 1 - This is 2.7% of all KS cases.
DEATHS: 3
Texas: 2 This is 0.31% of all cases
New Mexico: 1 This is 1.54% of all cases
US NATIONAL CASE COUNT: 967 (Confirmed and suspected):
INTERNATIONAL SPREAD (As of 4/2/2025)
Mexico 865 (+58)
Chihuahua, Mexico: 844 (+58) cases, 3 hospitalizations, 1 fatality
Canada: 1531 (+270) (This reflects Ontario's Outbreak, which began 11/24)
Ontario, Canada 1243 (+223) cases, 84 hospitalizations.
Europe: 6,814
03#UNTAGGED. Generosity in architecture.
03#UNTAGGED. Generosity in architecture.MCH
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What makes space feel generous, and how architecture address this generosity in terms of atmosphere, metrics, and the implications of its scale? This edition of #Untagged explores these and other questions in its presentation of the 2024 edition of the Master in Collective Housing. The Master of Architecture in Collective Housing, MCH, is a postgraduate full-time international professional program of advanced architecture design in collective housing presented by Universidad Polit辿cnica of Madrid (UPM) and Swiss Federal Institute of Technology (ETH).
Yearbook MCH 2024. Master in Advanced Studies in Collective Housing UPM - ETH
Junction Field Effect Transistors (JFET)
Junction Field Effect Transistors (JFET)GS Virdi
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In this concise presentation, Dr. G.S. Virdi (Former Chief Scientist, CSIR-CEERI, Pilani) introduces the Junction Field-Effect Transistor (JFET)a cornerstone of modern analog electronics. Youll discover:
Why JFETs? Learn how their high input impedance and low noise solve the drawbacks of bipolar transistors.
JFET vs. MOSFET: Understand the core differences between JFET and MOSFET devices.
Internal Structure: See how source, drain, gate, and the depletion region form a controllable semiconductor channel.
Real-World Applications: Explore where JFETs power amplifiers, sensors, and precision circuits.
Perfect for electronics students, hobbyists, and practicing engineers looking for a clear, practical guide to JFET technology.The History of Kashmir Karkota Dynasty NEP.pptx
The History of Kashmir Karkota Dynasty NEP.pptxArya Mahila P. G. College, Banaras Hindu University, Varanasi, India.
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This slide is an exercise for the inquisitive students preparing for the competitive examinations of the undergraduate and postgraduate students. An attempt is being made to present the slide keeping in mind the New Education Policy (NEP). An attempt has been made to give the references of the facts at the end of the slide. If new facts are discovered in the near future, this slide will be revised.
This presentation is related to the brief History of Kashmir (Part-I) with special reference to Karkota Dynasty. In the seventh century a person named Durlabhvardhan founded the Karkot dynasty in Kashmir. He was a functionary of Baladitya, the last king of the Gonanda dynasty. This dynasty ruled Kashmir before the Karkot dynasty. He was a powerful king. Huansang tells us that in his time Taxila, Singhpur, Ursha, Punch and Rajputana were parts of the Kashmir state.Biophysics Chapter 3 Methods of Studying Macromolecules.pdf
Biophysics Chapter 3 Methods of Studying Macromolecules.pdfPKLI-Institute of Nursing and Allied Health Sciences Lahore , Pakistan.
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YSPH VMOC Special Report - Measles Outbreak Southwest US 5-3-2025.pptx
YSPH VMOC Special Report - Measles Outbreak Southwest US 5-3-2025.pptxYale School of Public Health - The Virtual Medical Operations Center (VMOC)
油
The History of Kashmir Karkota Dynasty NEP.pptx
The History of Kashmir Karkota Dynasty NEP.pptxArya Mahila P. G. College, Banaras Hindu University, Varanasi, India.
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M 1.5 p4.q
- 1. P4: speaks the truth out of times. A die is tossed. He reports that there is a six. What is the chance that actually there was six.