This document provides an overview of random variables and probability distributions. It covers key concepts such as defining random variables as either discrete or continuous, constructing probability distributions that show the possible values and probabilities of random variables, and calculating metrics like the mean and variance. Examples discussed include the number of defective cell phones from a sample, with probabilities of 0, 1, 2, or 3 defective phones calculated. Formulas are provided for finding the mean, variance, and computing general probabilities from a probability distribution.
Determining the Mean, Variance, and Standard Deviation of a Discrete Random Variable
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs
Probability Distribution (Discrete Random Variable)Cess011697
Learning Competencies:
- to find the possible values of a random variable.
illustrates a probability distribution for a discrete random variable and its properties.
- to compute probabilities corresponding to a given random variable.
There are some exercises for you to answer.
Random Variable (Discrete and Continuous)Cess011697
Learning Competencies
- to recall statistical experiment and sample space
- to illustrate a random variable (discrete and continuous).
- to distinguish between a discrete and a continuous random variable.
Determining the Mean, Variance, and Standard Deviation of a Discrete Random Variable
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs
Probability Distribution (Discrete Random Variable)Cess011697
Learning Competencies:
- to find the possible values of a random variable.
illustrates a probability distribution for a discrete random variable and its properties.
- to compute probabilities corresponding to a given random variable.
There are some exercises for you to answer.
Random Variable (Discrete and Continuous)Cess011697
Learning Competencies
- to recall statistical experiment and sample space
- to illustrate a random variable (discrete and continuous).
- to distinguish between a discrete and a continuous random variable.
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about functions and its operations such as addition, subtraction, multiplication, division and composition. It is also comprised of some examples and exercises to be done for the said topic.
Discrete and COntinuous Random Variable with Game for Motivation
distinguish between a discrete and a continuous random variable.
find possible values of random variable
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about functions and its operations such as addition, subtraction, multiplication, division and composition. It is also comprised of some examples and exercises to be done for the said topic.
Discrete and COntinuous Random Variable with Game for Motivation
distinguish between a discrete and a continuous random variable.
find possible values of random variable
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
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.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Overview on Edible Vaccine: Pros & Cons with Mechanism
Random Variables and Probabiity Distribution
1. TOPIC 1: RANDOM VARIABLES
AND PROBABILITY
DISTRIBUTION
PREPARED BY: JESSA R. ALBIT
2. LESSON 1: EXPLORING RANDOM VARIABLES
LESSON OBJECTIVES:
AT THE END OF THIS LESSON, YOU ARE EXPECTED TO:
• ILLUSTRATE A RANDOM VARIABLE;
• CLASSIFY RANDOM VARIABLES AS DISCRETE OR CONTINUOUS; AND
• FIND THE POSSIBLE VALUES OF A RANDOM VARIABLE.
4. MOTIVATION
EXPIREMENT OUTCOMES SAMPLE SPACE
TOSS A COIN ONCE HEAD, TAIL
TOSS A COIN TWICE HH, HT, TH, TT
ROLL A DIE 1, 2, 3, 4, 5, 6
EXAM RESULT PASS, FAIL
GAME RESULT WIN, LOSE
5. MOTIVATION
EXPIREMENT OUTCOMES SAMPLE SPACE
TOSS A COIN ONCE HEAD, TAIL 𝑆 = 𝐻𝐸𝐴𝐷, 𝑇𝐴𝐼𝐿
TOSS A COIN TWICE HH, HT, TH, TT
𝑆
= HH, HT, TH, TT
ROLL A DIE 1, 2, 3, 4, 5, 6
𝑆
= 1, 2, 3, 4, 5, 6
EXAM RESULT PASS, FAIL 𝑆 = PASS, FAIL
GAME RESULT WIN, LOSE 𝑆 = WIN, LOSE
6. DEFECTIVE CELLPHONES
Suppose three cell phones are tested at random. We want to find out
the number of defective cell phones that occur. Thus, to each outcome
in the same space we shall assign a value. These are 0, 1, 2, or 3. If there
is no defective cell phone, we assign the number 0; if there is 1
defective cell phone, we assign the number 1; if there are two defective
cell phones, we assign 2; and 3, if there is three defective cell phones.
The number of defective cell phones is a random variable. The possible
values of this random variable are 0, 1, 2, and 3.
8. LET’S COMPLETE THE TABLE BELOW
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE X
9. LET’S COMPLETE THE TABLE BELOW
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE X
NNN 0
NND 1
NDN 1
DNN 1
NDD 2
DND 2
DDN 2
DDD 3
SO, THE POSSIBLE VALUES OF THE RANDOM VARIABLE X ARE 0, 1, 2, AND 3.
10. RANDOM VARIABLE
• A RANDOM VARIABLE IS A FUNCTION THAT ASSOCIATES A REAL
NUMBER TO EACH ELEMENT IN THE SAMPLE SPACE. IT IS A VARIABLE
WHOSE VALUES ARE DETERMINED BY CHANCE
12. ACTIVITY
GIVEN DISCRETE OR CONTINUOUS
THE PRICE OF A HOUSE.
TIME TO DOWNLOAD A WEBPAGE.
ADVERTISING EXPENDITURES OF A
COMPANY.
STUDENT ENROLLMENT IN A CERTAIN
UNIVERSITY.
WATER TEMPERATURE OF NILE RIVER.
13. ACTIVITY
GIVEN DISCRETE OR CONTINUOUS
THE PRICE OF A HOUSE. DISCRETE
TIME TO DOWNLOAD A WEBPAGE. CONTINUOUS
ADVERTISING EXPENDITURES OF A COMPANY. DISCRETE
STUDENT ENROLLMENT IN A CERTAIN UNIVERSITY. DISCRETE
WATER TEMPERATURE OF NILE RIVER. CONTINUOUS
14. TRY THIS!
• SUPPOSE THREE COINS ARE TOSSED. LET Y BE THE RANDOM
VARIABLE REPRESENTING THE NUMBER OF TAILS THAT OCCUR.
FIND THE PROBABILITY OF EACH OF THE VALUES OF THE
RANDOM VARIABLE Y.
16. LESSON 2: CONSTRUCTING PROBABILITY
DISTRIBUTION
LESSON OBJECTIVES:
AT THE END OF THE LESSON, YOU SHOULD BE ABLE TO:
• ILLUSTRATE A PROBABILITY DISTRIBUTION FOR A DISCRETE RANDOM
VARIABLE AND ITS PROPERTIES;
• COMPUTE PROBABILITIES CORRESPONDING TO A GIVEN RANDOM
VARIABLE,; AND
• CONSTRUCT THE PROBABILITY MASS FUNCTION OF A DISCRETE
RANDOM VARIABLE AND ITS CORRESPONDING HISTOGRAM.
17. DISCRETE PROBABILTY DISTRIBUTION
• A DISCRETE PROBABILITY DISTRIBUTION OR A PROBABILITY MASS
FUNCTION CONSISTS OF THE VALUES A RANDOM VARIABLE CAN
ASSUME AND THE CORRESPONDING PROBABILITIES OF THE VALUES.
18. USING THE SAME THE DATA FROM LESSON1, LET’S
CONSTRUCT THE PROBABILITY DISTRIBUTION.
19. DEFECTIVE CELLPHONES
Suppose three cell phones are tested at random. We want to find out
the number of defective cell phones that occur. Thus, to each outcome
in the same space we shall assign a value. These are 0, 1, 2, or 3. If there
is no defective cell phone, we assign the number 0; if there is 1
defective cell phone, we assign the number 1; if there are two defective
cell phones, we assign 2; and 3, if there is three defective cell phones.
The number of defective cell phones is a random variable. The possible
values of this random variable are 0, 1, 2, and 3.
21. LET’S COMPLETE THE TABLE BELOW
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE X
NNN 0
NND 1
NDN 1
DNN 1
NDD 2
DND 2
DDN 2
DDD 3
SO, THE POSSIBLE VALUES OF THE RANDOM VARIABLE X ARE 0, 1, 2, AND 3.
25. PROPERTIES OF A PROBABILITY DISTRIBUTION
1. THE PROBABILTY OF EACH VALUE OF A RANDOM VARIABLE MUST BE BETWEEN
OR EQUAL TO 0 AND 1. IN SYMBOL, WE WRITE IT AS 0 ≤ 𝑃 𝑋 ≤ 1.
2. THE SUM OF THE PROBABILITIES OF ALL VALUES OF THE RANDOM VARIABLE
MUST BE EQUAL TO 1. IN SYMBOL, WE WRITE IT AS 𝑃 𝑋 = 1.
26. LESSON 3: COMPUTING THE MEAN OF A
DISCRETE PROBABILITY DISTRIBUTION
LESSON OBJECTIVES:
AT THE END OF THIS LESSON, YOU SHOULD BE ABLE TO:
• ILLUSTRATE AND CALCULATE THE MEAN OF A DISCRETE RANDOM
VARIABLE;
• INTERPRET THE MEAN OF A DISCRETE RANDOM VARIABLE; AND
• SOLVE PROBLEMS INVOLVING MEAN OF PROBABILITY
DISTRIBUTIONS.
28. STEP 1: CONSTRUCT PROBABILITY
DISTRIBUTION
NUMBER OF DEFECTIVE CELLPHONES
X
P(X)
0
1
8
1
3
8
2
3
8
3
1
8
TOTAL
8
8
= 1
29. STEP 2:
NUMBER OF DEFECTIVE
CELLPHONES
X
P(X) X* P(X)
0
1
8
0 ×
1
8
= 0
1
3
8
3
8
2
3
8
6
8
3
1
8
3
8
TOTAL
8
8
= 1 𝜇 = 𝑋 ∗ 𝑃 𝑋 =
0
8
+
3
8
+
6
8
+
3
8
=
12
8
= 1.5
STEP 3
SO, THE AVERAGE NUMBER OF DEFECTIVE CELLPHONES THAT
IS TESTED IS 1.5
30. LESSON 4: COMPUTING THE VARIANCE OF A
DISCRETE PRO
LESSON OBJECTIVES:
AT THE END OF THIS LESSON, YOU SHOULD BE ABLE TO:
• ILLUSTRATE AND CALCULATE THE VARIANCE OF A DISCRETE RANDOM
VARIABLE;
• INTERPRET THE VARIANCEOF A DISCRETE RANDOM VARIABLE; AND
• SOLVE PROBLEMS INVOLVING VARIANCE OF PROBABILITY
DISTRIBUTIONS.