This powerpoint was used in my 7th and 8th grade classes to review the fundamental counting principle used in our probability unit. There are three independent practice problems at the end.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
Introduction to Sets and Set Operations. The presentation include contents of a KWLH Chart, Essential Questions, and Self-Assessment Questions. With exploration and formative assessments.
A random variable is a mathematical concept used to describe the outcome of a random process or experiment. It is a variable that takes on different values based on the outcome of a random event. In mathematical terms, a random variable is a function that maps the outcomes of a random experiment to a set of real numbers.
There are two types of random variables: discrete and continuous. A discrete random variable can take on only a finite or countably infinite number of values, such as the number of heads in a sequence of coin flips. A continuous random variable, on the other hand, can take on any value within a given range, such as the height of a person.
The probability distribution of a random variable defines the likelihood of each possible outcome of the random process or experiment. For a discrete random variable, this is represented by a probability mass function (PMF), which gives the probability of each possible outcome. For a continuous random variable, the probability distribution is represented by a probability density function (PDF), which gives the relative likelihood of different outcomes within a given range.
Another important concept in the study of random variables is expected value, also known as the mean or average of a random variable. The expected value represents the long-term average of the values that a random variable takes on, and is calculated as the weighted sum of the possible values, where the weights are the probabilities of each outcome.
Random variables are used in a variety of mathematical and statistical applications, including decision theory, finance, and quality control. They also play a central role in the study of probability and statistics, and are used to model and analyze complex systems and phenomena in fields such as physics, engineering, and economics.
In conclusion, random variables are a powerful tool for describing the outcomes of random processes and experiments, and provide a framework for understanding the probabilistic behavior of complex systems. Understanding and using random variables is essential for making informed decisions and solving problems in a variety of fields and applications.A random variable is a mathematical concept that describes the outcome of a random event. It is a variable that can take on different values based on the outcome of the event. There are two types of random variables: discrete and continuous. A discrete random variable can take on only a finite or countably infinite number of values, such as the number of heads in a sequence of coin flips. A continuous random variable, on the other hand, can take on any value within a given range, such as the height of a person. The probability distribution of a random variable defines the likelihood of each possible outcome and is used to calculate the expected value, which is the long-term average of the values that a random variable takes on. Random variables are widely used in mathematics and statistics, and are essen
Experiment
Event
Sample Space
Unions and Intersections
Mutually Exclusive Events
Rule of Multiplication
Rule of Permutation
Rule of Combination
PROBABILITY
This powerpoint was used in my 7th and 8th grade classes to review the fundamental counting principle used in our probability unit. There are three independent practice problems at the end.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
Introduction to Sets and Set Operations. The presentation include contents of a KWLH Chart, Essential Questions, and Self-Assessment Questions. With exploration and formative assessments.
A random variable is a mathematical concept used to describe the outcome of a random process or experiment. It is a variable that takes on different values based on the outcome of a random event. In mathematical terms, a random variable is a function that maps the outcomes of a random experiment to a set of real numbers.
There are two types of random variables: discrete and continuous. A discrete random variable can take on only a finite or countably infinite number of values, such as the number of heads in a sequence of coin flips. A continuous random variable, on the other hand, can take on any value within a given range, such as the height of a person.
The probability distribution of a random variable defines the likelihood of each possible outcome of the random process or experiment. For a discrete random variable, this is represented by a probability mass function (PMF), which gives the probability of each possible outcome. For a continuous random variable, the probability distribution is represented by a probability density function (PDF), which gives the relative likelihood of different outcomes within a given range.
Another important concept in the study of random variables is expected value, also known as the mean or average of a random variable. The expected value represents the long-term average of the values that a random variable takes on, and is calculated as the weighted sum of the possible values, where the weights are the probabilities of each outcome.
Random variables are used in a variety of mathematical and statistical applications, including decision theory, finance, and quality control. They also play a central role in the study of probability and statistics, and are used to model and analyze complex systems and phenomena in fields such as physics, engineering, and economics.
In conclusion, random variables are a powerful tool for describing the outcomes of random processes and experiments, and provide a framework for understanding the probabilistic behavior of complex systems. Understanding and using random variables is essential for making informed decisions and solving problems in a variety of fields and applications.A random variable is a mathematical concept that describes the outcome of a random event. It is a variable that can take on different values based on the outcome of the event. There are two types of random variables: discrete and continuous. A discrete random variable can take on only a finite or countably infinite number of values, such as the number of heads in a sequence of coin flips. A continuous random variable, on the other hand, can take on any value within a given range, such as the height of a person. The probability distribution of a random variable defines the likelihood of each possible outcome and is used to calculate the expected value, which is the long-term average of the values that a random variable takes on. Random variables are widely used in mathematics and statistics, and are essen
Experiment
Event
Sample Space
Unions and Intersections
Mutually Exclusive Events
Rule of Multiplication
Rule of Permutation
Rule of Combination
PROBABILITY
Presentation given at the 3rd International Workshop on Cognition: Interdisciplinary Foundations, Models and Applications (CIFMA2021), joint with SEFM 2021
Pecha kucha: ratios, proportions, and probabilityBrent Edward
A Pecha Kucha (20 slides in 6 minutes) presentation meant to be a useful introduction and overview for a 7th grade middle school mathunit on Ratios, Proportions, and Probability
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
6. What is probability?
• Mathematical machinery to deal with
uncertain events
• What does uncertain mean?
• What is an event?
7. Random experiment
An observation that is uncertain:
we don’t know ahead of time what the
answer will be (pretty common!)
Ideally we want the experiment to be
repeatable under exactly the same initial
conditions (pretty rare!)
8. Sample space
A set containing all possible outcomes
from an experiment. Often called S.
An event is a subset of the sample space
9. Random experiments
• The sequence of dice • The length of time until
rolls until you get a six your next sneeze
• The weather tomorrow • My age
• The next hand in a • The result of a coin flip
poker game
• The weight of a bag of
• Your final grade in this m&m’s
class
• The sex of a randomly
• The next President of selected member of
the United States class
10. Your turn
• How could you classify these different
experiments based on the sample
space?
• Think (2 min)
• Pair (3 min)
• Square (3 min)
• Share (2 min)
12. Cardinality
• Small (< 10)
• Large, but finite
• Countably infinite
• Uncountably infinite
• We will follow this order as we develop
increasingly complex mathematical
tools
13. Events
• An event is a subset of the sample
space
• Set of all possible events is the
power set of S
• Examples
14. Set algebra
• Intersection and union are:
• Commutative (order from left to right doesn’t matter)
• Associative (order of operation doesn’t matter)
• Distributive (can expand brackets)
• You should be familiar with everything
on: http://en.wikipedia.org/wiki/Algebra_of_sets
16. How do we define
uncertainty?
• Associate a probability with each
element of the sample space.
• Defined by the function probability
mass function (pmf).
• The probability is the long run relative
frequency
17. Properties of pmf
• What are some properties that the pmf
must have? (Use your common sense)
• For example, take the random
experiment of flipping two coins and
observing whether they come up heads
or tails. How are the probabilities of
the different events related?
18. Properties of pmf
• Basic (as defined by book)
• Important derived properties
(T 1.2-1 - T1.2-6)
• Strategies of T1.2-3 and T1.2-5
particularly important
