The document discusses key concepts in probability, including analytic, frequentist, and subjective views of probability. It covers terms like events, independence, dependent events, mutually exclusive events, and exhaustive events. Laws of probability like the additive law and multiplicative law are explained. Examples are provided to demonstrate calculating probabilities using tables and the normal distribution. The central limit theorem and law of large numbers are introduced.
This is about the correlation analysis in statistics. It covers types, importance,Scatter diagram method
Karl pearson correlation coefficient
Spearman rank correlation coefficient
Mathematics, Statistics, Probability, Randomness, General Probability Rules, General Addition Rules, Conditional Probability, General Multiplication Rules, Bayes’s Rule, Independence
This is about the correlation analysis in statistics. It covers types, importance,Scatter diagram method
Karl pearson correlation coefficient
Spearman rank correlation coefficient
Mathematics, Statistics, Probability, Randomness, General Probability Rules, General Addition Rules, Conditional Probability, General Multiplication Rules, Bayes’s Rule, Independence
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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!
Embracing GenAI - A Strategic ImperativePeter 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.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
2. Analytic View of
Probability
If an event can occur in A ways and can fail
to occur in B ways, and if all possible
outcomes are equally likely to occur, then:
Occurrence:
A/(A+B)
Fail to Occur:
B/(A+B)
3. Frequentist View of
Probability
Probability is defined in terms of one’s past
performance
Uses sampling with replacement/independent
random sampling
5. Key Terms
• Data used in analyzing probability
• Outcome of trial
Event
• Occurrence of one event is not dependent on the other
Independent Events
• Outcome of one event is related to the other
Dependent Events
• One way only
Mutually Exclusive Events
• All possible events
Exhaustive Events
6. Laws of Probability
The probability of the occurrence of one event or another is equal
to the sum of their separate probabilities.
Additive Law
The probability of the joint occurrence of two or more
independent events is the product of their individual probabilities.
Multiplicative
Law
Co-occurrence of two events
Joint Probability
The probability that one event will occur given the occurrence of
some other event.
Conditional
Probability
The probability of one event ignoring the occurrence or
nonoccurrence of some other event.
Unconditional
Probability
7. Laws of Probability: An
Example
Income and Happiness: Is there a
relationship?
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
8. Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT IS NOT TOO HAPPY?
p
p = 315/1993 = 0.16
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
9. Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS A BELOW AVERAGE
INCOME?
p
p = 687/1993 = 0.34
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
10. Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS AN AVERAGE INCOME AND
IS PRETTY HAPPY?
p = 473/1993 = 0.24
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
11. Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A
PARTICIPANT HAS A BELOW AVERAGE
INCOME GIVEN THAT HE/SHE IS VERY HAPPY?
p = 132/687 = 0.19
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
12. Laws of Probability: An
Example
WHAT IS THE PROBABILITY THAT A PARTICIPANT HAS A
BELOW AVERAGE INCOME AND IS NOT TOO HAPPY?
p = 687/1993 = 0.34
p = 315/1993 = 0.16
p = (0.34) x (0.16) = 0.05
INCOME VERY
HAPPY
PRETTY
HAPPY
NOT TOO
HAPPY
TOTAL
Above
Average
164 233 26 423
Average 293 473 117 883
Below
Average
132 383 172 687
TOTAL 589 1089 315 1993
13. The Normal Distribution
Symmetrical
Bell-shaped
Mean, Median, and Mode are equal to one
another
15. The Normal Distribution
The use of z-scores can help determine the
probability
Can describe the proportions of area
contained in each section of the distribution
16. The Normal Distribution
The use of z-scores can help determine the
probability
Can describe the proportions of area
contained in each section of the distribution
17. z-scores
Helps identify the exact location of a score
in a distribution
To make raw scores meaningful, they are
transformed into new values
Standardizes the entire distribution
19. Example 1
SAT scores for a normal distribution with
mean of 500 and a standard deviation of 100.
What SAT score separates the top 10% of the
distribution from the test?
20. Solution 1
X = mean + (z) (sd)
X = 500 + (z) (100)
X = 500 + (1.28) (100)
X = 500 + 128
X = 628
21. Example 2
IQ test scores are standardized to produce a
normal distribution with a mean of 100 and a
standard deviation of 15. Find the proportion
of the population in each of the following IQ
categories:
Genius or near genius: IQ over 140
Very superior: IQ 120-140
Average: IQ 90-109
22. Solution 2
Genius or near genius:
z = 140-100/15
z = 2.67
p = 0.0038 or 3.8%
Very Superior:
z = 120-100/15 = 1.33
z = 140-100/15 = 2.67
p (120 < X < 140) = 0. 0918 – 0.0038
p = 0.0880 or 8.8%
Average:
z = 90-100/15 = -0.67
z = 109-100/15 = 0.60
p = (90 < X < 109) = 0.2486 + 0.2257
p = 0.4744 or 47.44%
23. Sampling Error
Discrepancy between a sample statistic and
its corresponding population parameter
If the population is normal, you should be
able to determine the probability of
obtaining any individual score
25. Distribution of Sample
Means
Collection of sample means for all possible
random samples of a particular size that can
be obtained from a population
Characteristics:
Piles up around population mean
Forms a normal distribution
The larger the sample size, the closer to the
population mean
26. Central Limit Theorem
For any population with mean and standard
deviation, the distribution of sample means
for sample size will have a mean and a
standard deviation ( 𝜎 𝑛) that will
approach a normal distribution as the
sample approaches infinity.
27. Central Limit Theorem
Expected Value of M
The mean of the distribution of sample
means is equal to the mean of the
population of scores
Standard Error of M
Provides a measure on how much distance is
expected between sample mean and population
mean
28. Law of Large Numbers
The larger the sample size, the more
probable it is that the sample mean will be
close to the population mean
When n > 30, the distribution is almost
normal regardless of the shape
As sample size increases, error decreases