1. Continuous random variables are defined over intervals rather than discrete points. The probability that a continuous random variable takes on a value in an interval from a to b is given by an integral of the probability density function f(x) over that interval.
2. The probability density function f(x) defines the probabilities of intervals of the continuous random variable rather than individual points. It has the properties that it is always nonnegative and its integral over all values is 1.
3. The cumulative distribution function F(x) gives the probability that the random variable takes on a value less than or equal to x. It is defined as the integral of the probability density function from negative infinity to x.
: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
This presentation contains the topic as follows, probability distribution, random variable, continuous variable, discrete variable, probability mass function, expected value and variance and examples
: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
This presentation contains the topic as follows, probability distribution, random variable, continuous variable, discrete variable, probability mass function, expected value and variance and examples
Opciones de Cobertura de Salud Para las Familias Inmigrantes: ¡Tres Preguntas...Alejandrina E. Ricardez
Tres Preguntas:
¿Cuáles son las opciones de cobertura de salud médica para mí y para mi familia?
¿Qué es lo que necesito hacer para mantener la cobertura de salud médica?
¿Cómo es que la cobertura de salud médica afecta el estatus migratorio?
Contestar preguntas y respuestas
Recursos
Opciones de Cobertura de Salud Para las Familias Inmigrantes: ¡Tres Preguntas...Alejandrina E. Ricardez
Tres Preguntas:
¿Cuáles son las opciones de cobertura de salud médica para mí y para mi familia?
¿Qué es lo que necesito hacer para mantener la cobertura de salud médica?
¿Cómo es que la cobertura de salud médica afecta el estatus migratorio?
Contestar preguntas y respuestas
Recursos
Random variables and probability distributions Random Va.docxcatheryncouper
Random variables and probability distributions
Random Variable
The outcome of an experiment need not be a number, for example, the outcome when a
coin is tossed can be 'heads' or 'tails'. However, we often want to represent outcomes
as numbers. A random variable is a function that associates a unique numerical value
with every outcome of an experiment. The value of the random variable will vary from
trial to trial as the experiment is repeated.
There are two types of random variable - discrete and continuous.
A random variable has either an associated probability distribution (discrete random
variable) or probability density function (continuous random variable).
Examples
1. A coin is tossed ten times. The random variable X is the number of tails that are
noted. X can only take the values 0, 1, ..., 10, so X is a discrete random variable.
2. A light bulb is burned until it burns out. The random variable Y is its lifetime in
hours. Y can take any positive real value, so Y is a continuous random variable.
Expected Value
The expected value (or population mean) of a random variable indicates its average or
central value. It is a useful summary value (a number) of the variable's distribution.
Stating the expected value gives a general impression of the behaviour of some random
variable without giving full details of its probability distribution (if it is discrete) or its
probability density function (if it is continuous).
Two random variables with the same expected value can have very different
distributions. There are other useful descriptive measures which affect the shape of the
distribution, for example variance.
The expected value of a random variable X is symbolised by E(X) or µ.
If X is a discrete random variable with possible values x1, x2, x3, ..., xn, and p(xi)
denotes P(X = xi), then the expected value of X is defined by:
where the elements are summed over all values of the random variable X.
http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#discvar
http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#contvar
http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#variance
If X is a continuous random variable with probability density function f(x), then the
expected value of X is defined by:
Example
Discrete case : When a die is thrown, each of the possible faces 1, 2, 3, 4, 5, 6 (the xi's)
has a probability of 1/6 (the p(xi)'s) of showing. The expected value of the face showing
is therefore:
µ = E(X) = (1 x 1/6) + (2 x 1/6) + (3 x 1/6) + (4 x 1/6) + (5 x 1/6) + (6 x 1/6) = 3.5
Notice that, in this case, E(X) is 3.5, which is not a possible value of X.
See also sample mean.
Variance
The (population) variance of a random variable is a non-negative number which gives
an idea of how widely spread the values of the random variable are likely to be; the
larger the variance, the more scattered the obser ...
Let n be a non-negative integer and a and c be positive numbers. Use.pdfairtechsalesservices
Let n be a non-negative integer and a and c be positive numbers. Use probability to express
0a xne-cxdx in terms of a finite sum.
Solution
F(x) = P(X x) (also denoted FX(x)). F(x) is the cumulative probability to the left of
(and including) the point x. The survival function is the complement of the distribution function,
S(x) = 1 - F(x) = P(X > x). For a discrete random variable with probability function p(x), F(x) =
X wx p(w), and in this case F(x) is a step function (it has a jump at each point with non-zero
probability, while remaining constant until the next jump). If X has a continuous distribution
with density function f(x), then F(x) = R x -1 f(t)dt and F(x) is a continuous, differentiable, non-
decreasing function such that d dxF(x) = F0(x) = -S0(x) = f(x). If X has a mixed distribution,
then F(x) is continuous except at the points of non-zero probability mass, where F(x) will have a
jump. For any cdf P(a < X < b) = F(b) - F(a), lim x!1 F(x) = 1, lim x!-1 F(x) = 0..
Probability
Random variables and Probability Distributions
The Normal Probability Distributions and Related Distributions
Sampling Distributions for Samples from a Normal Population
Classical Statistical Inferences
Properties of Estimators
Testing of Hypotheses
Relationship between Confidence Interval Procedures and Tests of Hypotheses.
A polynomial interpolation algorithm is developed using the Newton's divided-difference interpolating polynomials. The definition of monotony of a function is then used to define the least degree of the polynomial to make efficient and consistent the interpolation in the discrete given function. The relation between the order of monotony of a particular function and the degree of the interpolating polynomial is justified, analyzing the relation between the derivatives of such function and the truncation error expression. In this algorithm there is not matter about the number and the arrangement of the data points, neither if the points are regularly spaced or not. The algorithm thus defined can be used to make interpolations in functions of one and several dependent variables. The algoritm automatically select the data points nearest to the point where an interpolation is desired, following the criterion of symmetry. Indirectly, the algorithm also select the number of data points, which is a unity higher than the order of the used polynomial, following the criterion of monotony. Finally, the complete algoritm is presented and subroutines in fortran code is exposed as an addendum. Notice that there is not the degree of the interpolating polynomial within the arguments of such subroutines.
ANURAG TYAGI CLASSES (ATC) is an organisation destined to orient students into correct path to achieve
success in IIT-JEE, AIEEE, PMT, CBSE & ICSE board classes. The organisation is run by a competitive staff comprising of Ex-IITians. Our goal at ATC is to create an environment that inspires students to recognise and explore their own potentials and build up confidence in themselves.ATC was founded by Mr. ANURAG TYAGI on 19 march, 2001.
VISIT US @
www.anuragtyagiclasses.com
ANURAG TYAGI CLASSES (ATC) is an organisation destined to orient students into correct path to achieve
success in IIT-JEE, AIEEE, PMT, CBSE & ICSE board classes. The organisation is run by a competitive staff comprising of Ex-IITians. Our goal at ATC is to create an environment that inspires students to recognise and explore their own potentials and build up confidence in themselves.ATC was founded by Mr. ANURAG TYAGI on 19 march, 2001.
VISIT US @
www.anuragtyagiclasses.com
Density function in probability or density of any continuous instantly selected variable is a function in which the count provided at given point (sample) in the available set of possibilities random values can be predicted as giving a linked or dependent prospect for a continuous unplanned variable would the same of that sample. Copy the link given below and paste it in new browser window to get more information on Density Function:- www.transtutors.com/homework-help/statistics/density-function.aspx
The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
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/
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
2. Continuous Random Variables Suppose we are interested in the probability that a given random variable will take on a value on the interval from a to b where a and b are constants with a b. First, we divide the interval from a to b into n equal subintervals of width x containing respectively the points x1, x2, … , xn. Suppose that the probability that the random variable will take on a value in subinterval containing xi is given by f(xi)x. Then the probability that the random variable will take on a value in the interval from a to b is given by
3. Continuous Random Variables(cont’d) If f is an integrable function defined for all values of the random variable, the probability that the value of the random variables falls between a and b is defined by letting x 0 as Note: The value of f(x) does not give the probability that the corresponding random variable takes on the values x; in the continuous case, probabilities are given by integrals not by the values f(x).
5. Continuous Random Variables(cont’d) The probability that a random variable takes on value x, i.e. Thus, in the continuous case probabilities associated with individual points are always zero. Consequently,
6. Continuous Random Variables(cont’d) The function f is called probability density function or simply probability density. Characteristics of the probability density function f : 1. for all x. 2. F(x) represents the probability that a random variable with probability density f(x) takes on a value less than or equal to x and the corresponding function F is called the cumulative distribution function or simply distribution function of the random variable X.
7. Continuous Random Variables(cont’d) Thus, for any value x, F (x) = P(X x) is the area under the probability density function over the interval - to x. Mathematically, The probability that the random variable will take on a value on the interval from a to b is given by P(a X b) = F (b) - F (a)
8. Continuous Random Variables(cont’d) According to the fundamental theorem of integral calculus it follows that wherever this derivative exists. F is non-decreasing function, F(-) = 0 and F() = 1. kth moment about the origin