1. Accuracy refers to how close measurements are to the true value, while precision refers to how close repeated measurements are to each other.
2. Measurements can be precise but not accurate if they are clustered around a value different from the true value, or accurate but not precise if widely dispersed around the true value.
3. Errors in measurement can be mistakes, systematic errors caused by natural or instrumental factors, or random errors that follow a normal distribution. The standard deviation describes the spread of random errors.
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
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PayPal ID is japhethmuthama@gmail.com
Please Subscribe to this Channel for more solutions and lectures
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
I am Bella A. I am a Statistical Method In Economics Assignment Expert at economicshomeworkhelper.com/. I hold a Ph.D. in Economics. I have been helping students with their homework for the past 9 years. I solve assignments related to Economics Assignment.
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To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
2. Accuracy × precision
The term accuracy refers to the closeness
between measurements and their true values.
The further a measurement is from its true
value, the less accurate it is.
As opposed to accuracy, the term precision is
related to the closeness to one another of a set
of repeated observation of a random variable.
If such observations are closely gathered
together, then they are said to have been
obtained with high precision.
2
3. It should be apparent that observations may be
precise but not accurate, if they are closely
grouped together but about a value that is
different from the true value by a significant
amount.
Also, observations may be accurate but not
precise if they are well distributed about the
true value but dispersed significantly from one
another.
3
4. Example – rifle shots
(a) – both accurate and precise
(b) – precise but not accurate
(c) – accurate but not precise
4
6. Mistakes
Mistakes actually are not errors because they
usually are so gross in size compared to the
other two types of errors. One of the most
common reasons for mistakes is simple
carelessness of the observer, who may take the
wrong reading of a scale or, if the proper value
was read, may record the wrong one by
transposing numbers, for example.
6
7. Systematic errors
Systematic errors or effects occur according to
a system that, if known, always can be
expressed by a mathematical formulation. Any
change in one or more of the elements of the
system will cause a change in the character of
the systematic effects if the observational
process is repeated. Systematic errors occur
due to natural causes, instrumental factors and
the observer’s human limitation.
7
8. Random errors
Random errors are unavoidable in so far as the
observer is concerned.
Example: if the true value of an angle is
41,1336 gon and the angle is measured 20
times, it is usual to get values for each of the
measurements that differ slightly from the true
angle. Each of these values has a probability
that it will occur. The closer the value
approaches 41,1336 gon, the higher is the
probability, and the farther away it is, the
lower is the probability. 8
9. Characteristics of random errors:
• probability of a plus and minus error of the
certain size is the same,
• probability of a small error is higher than
probability of a large error,
• errors larger than a certain limit do not occur
(they are considered to be mistakes).
The distribution of random errors is called
normal (Gauss) distribution and is interpreted
matematically with the Gauss curve →
9
10. E(x) - 2
σ
E(x) - 1
σ
ϕ(x)
E(x)
A
B
E(x) + 1
σ
E(x) + 2
σ
10
x
11. E(x) is expected value (unknown true value of a
quantity),
σ2 is variance = square of standard deviation.
It is not possible to find out the real value of a
quantity. The result of a measurement is the
most reliable value of a quantity and its
accuracy.
11
12. ε i = ∆i + ci
εi … real error of a measurement
Δi … random error
ci … systematic error
ε i = X − li
X … true (real) value of a quantity
li … measured value of a quantity
12
13. Processing of measurements with the
same accuracy
Specification of measurement accuracy =
standard deviation.
n
[ εε ] ∑εi 2
σ= = i =1
n n
n … number of measurements,
σ … if n → ∞,
s … if n is smaller number.
13
14. The true value of a quantity X is unknown
(→ the real error ε is also unknown).
Therefore the arithmetic mean is used as the
most probable estimation of X. The difference
between the average and a particular
measurement is called correction vi. The
standard deviation s is calculated using these
corrections.
n n
[ l] ∑li [ vv ] ∑v i
2
l = = i =1
vi = l − li s=
n −1
= i =1
n −1
n n
14
15. If the standard deviation of one measurement
is known and the measurement is carried out
more than once, the standard deviation of the
average is calculated according to the formula
σ
σl =
n
15
16. Processing of measurements with the
same accuracy – example
Problem: a distance was measured 5x under
the same conditions and by the same method
(= with the same accuracy). Measured values
are: 5,628; 5,626; 5,627; 5,624; 5,628 m.
Calculate the average distance, the standard
deviation of one measurement and the standard
deviation of the average.
16
17. Solution:
i l/m v/m vv / m2
1 5,628 -0,0014 1,96E-06
2 5,626 0,0006 3,60E-07
3 5,627 -0,0004 1,60E-07
4 5,624 0,0026 6,76E-06
5 5,628 -0,0014 1,96E-06
Σ 28,133 0,000 1,12E-05
l = 5,6266 m, sl = 0,0017 m, sl = 0,00075 m
i
17
18. Law of standard deviation propagation
Sometimes it is not possible to measure a value of
a quantity directly and then this value is
determined implicitly by calculation using other
measured values.
Examples:
• area of a triangle – two distances and an angle are
measured,
• height difference – a slope distance and a zenith
angle are measured.
18
19. If a mathematical relation between measured
and calculated values is known, the standard
deviation of the calculated value can be
derived using the law of standard deviation
propagation.
19
20. If a mathematical relation is known
y = f ( x1 , x2 , x3 , x4 ,..., x k )
then
y + ε y = f ( x1 + ε x1 , x2 + ε x2 , x3 + ε x3 , x4 + ε x4 ,..., xk + ε xk )
Real errors are much smaller than measured
values therefore the right part of the equation can
be expanded according to the Taylor’s expansion
(using terms of the first degree only).
20
22. Real errors of measured values are not usually
known but standard deviations are known.
The law of standard deviation propagation:
2 2 2 2
∂f 2 ∂f 2 ∂f 2 ∂f 2
σy =
2
÷ σ x1 + ÷ σ x2 + ÷ σ x3 + ... + ÷ σ xk
∂ x1 ∂ x2 ∂ x3 ∂ xk
22
23. It is possible to use the law of standard
deviation propagation if only:
1. Measured quantities are mutually independent.
2. Real errors are random.
3. Errors are much smaller than measured values.
4. There is the same unit of all terms.
23
24. Examples
Problem 1: the formula for a calculation of the
standard deviation of the average should be
derived if the standard deviation of one
measurement is known and all measurements
were carried out with the same accuracy
Solution: l1 + l2 + ...ln
l =
n
1
{
ε l = ε l1 + ε l2 + ... + ε ln
n
}
1 2
{
σ l = 2 σ l1 + σ l22 + ... + σ l2n
2
n
}
24
25. The real errors are random and generally different
ε l1 ≠ ε l2 ≠ ... ≠ ε ln
The standard deviations are the same for all
measurements
σ l2 = σ l2 = ... = σ l2 = σ l2
1 2 n
therefore
1 1 n 1 2
σ = 2 { σ l + σ l + ... + σ l } = 2 { n × l } = 2 { σ l } = σ l
2
l
2 2 2
σ 2 2
n n n n
1
σl = σl
n 25
26. Problem 2: two distances were measured in a
triangle a = 34,352 m, b = 28,311 m with the
accuracy σa = σb = 0,002 m. The horizontal
angle was also measured ω = 52,3452°, σω
= 0,0045°. Calculate the standard deviation of
the area of the triangle.
1
Solution: P = a ×b ×sin( ω )
2
1 1 1 π
ε P = b ×sin( ω ) ×ε a + a ×sin( ω ) ×ε b + a ×b ×cos( ω ) ×ε ω ×
2 2 2 180°
180°
ρ° =
π ÷ 26
27. 1 1 1 σω
2
σ P = ( b ×sin( ω )) × a + ( a ×sin( ω )) × b + ( a ×b ×cos( ω ) ) ×
2 2 2
2
σ2 σ2
( ρ°)
2
4 4 4
σ a = σ b = σ d:
1 2 1 σω
2
σP = ( b + a2 ) × 2 ( ω ) × d + ( a × ×
b cos( ω ) ) ×
2
2
sin σ2
( ρ°)
2
4 4
σP = 0,043 m2.
27