In this presentation we can get to know the meaning of basic discrete distribution for bivariate. There are also discussions regarding the topic along with marginal tables. Also there are certain illustrative example for the ease of understanding. Overall it is a great presentation for the junior engineers aiming in their course.
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
These slides represent a brief idea about conditional probability along with illustrative examples and discussions. It also consists the use of sets to develop a better understanding for the students having the following theorem in their course.
2.2 Special types of Correlation
2.3 Point Biserial Correlation rPB
2.3.1 Calculation of rPB
2.3.2 Significance Testing of rPB
2.4 Phi Coefficient (φ )
2.4.1 Significance Testing of phi (φ )
2.5 Biserial Correlation
2.6 Tetrachoric Correlation
2.7 Rank Order Correlations
2.7.1 Rank-order Data
2.7.2 Assumptions Underlying Pearson’s Correlation not Satisfied
2.8 Spearman’s Rank Order Correlation or Spearman’s rho (rs)
2.8.1 Null and Alternate Hypothesis
2.8.2 Numerical Example: for Untied and Tied Ranks
2.8.3 Spearman’s Rho with Tied Ranks
2.8.4 Steps for rS with Tied Ranks
2.8.5 Significance Testing of Spearman’s rho
2.9 Kendall’s Tau (ô)
2.9.1 Null and Alternative Hypothesis
2.9.2 Logic of Kendall’s Tau and Computation
2.9.3 Computational Alternative for Kendall’s Tau
2.9.4 Significance Testing for Kendall’s Tau
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
These slides represent a brief idea about conditional probability along with illustrative examples and discussions. It also consists the use of sets to develop a better understanding for the students having the following theorem in their course.
2.2 Special types of Correlation
2.3 Point Biserial Correlation rPB
2.3.1 Calculation of rPB
2.3.2 Significance Testing of rPB
2.4 Phi Coefficient (φ )
2.4.1 Significance Testing of phi (φ )
2.5 Biserial Correlation
2.6 Tetrachoric Correlation
2.7 Rank Order Correlations
2.7.1 Rank-order Data
2.7.2 Assumptions Underlying Pearson’s Correlation not Satisfied
2.8 Spearman’s Rank Order Correlation or Spearman’s rho (rs)
2.8.1 Null and Alternate Hypothesis
2.8.2 Numerical Example: for Untied and Tied Ranks
2.8.3 Spearman’s Rho with Tied Ranks
2.8.4 Steps for rS with Tied Ranks
2.8.5 Significance Testing of Spearman’s rho
2.9 Kendall’s Tau (ô)
2.9.1 Null and Alternative Hypothesis
2.9.2 Logic of Kendall’s Tau and Computation
2.9.3 Computational Alternative for Kendall’s Tau
2.9.4 Significance Testing for Kendall’s Tau
JEE Mathematics/ Lakshmikanta Satapathy/ Theory of Probability part 9 which explains Random variables , its probability distribution, Mean of a random variable and Variance of a random variable
Signal Constellation, Geometric Interpretation of SignalsArijitDhali
This is a handy presentation consisting the graphical and geometrical representation. Describing about orthonormality in a brief, along with basic vector and signal space. Also describing the QPSK constellation diagram and types of QPSK.
This presentation depicts the definition of stack, queue and subroutine. It s a minute presentation best for engineering students as well as reference for last minute notes or term paper presentation. Share and Help others .
Overviewing the techniques of Numerical Integration.pdfArijitDhali
In this presentation we discuss the ways of integrating a function using trapezoidal, simpsons 1/3,3/8 and boole's method. We also discussed its error and analysised other ways to solve it than mention.
In this presentation we discussed about the motorola's microprocessor 68020. Discussing about its architecture, technical data, history, literature survey. Also we discussed the visuals of registers, connections and pin diagrams.
Stereotactic Radiosurgery in Brain Metastases.pdfArijitDhali
Stereotactic radiosurgery (SRS) as a local high precision approach for the primary treatment of asymptomatic brain metastases (cancer) has gained wide acceptance. It leads to lasting tumor control with only minor side effects compared to whole brain radiotherapy, since there is only little dose delivered to the healthy brain.
In this presentation we discuss about the active filters and mentioned its frequency response along with block diagrams. Also discussed its pros and cons in this presentation.
In this presentation we discuss about a particular type of analog communication waves that is wideband frequency modulation. In this slide, its expression is discussed along with graphical visuals. Not forgetting its power and bandwidth as well. We also see the use of bessel function and the block diagrams that help to form this type of waves.
In this following presentation, one can get an idea for solving a common celebrity problem. It has general algorithm along with pseudocode, the code and the methods of solving it. It also discusses the time complexity in each step for better graphical representation.
SSBSC Single Side Band - Suppressed Carrier CompressedArijitDhali
This PowerPoint presentation is all about the definition of SSBSC or Single Side Band Suppressed Carrier. It consists of rich visuals along with the technique of modulation. Also a simplified version of derived expressions help the student to understand more about the topic. Moreover its suitable for students aiming for electronics and communication engineering.
This presentation is a depiction of ecological biodiversity in India. It includes basic understanding the meaning of biodiversity, discussing about the 4 hotspots in India, also discussing the habitat if each hotspots. A map is represented as well to know the locations of the hotspots, and the threatens are also discussed along with the solutions. Overall this is an outstanding nature based project with attractive visuals to stick the eyes of viewer to the presentation.
In this presentation we can know across the LTI systems. Also classifying the system and defining it. Also there has been a basic graphical image to help understanding. Mathematical theorems are also provided in it. Overall its a small presentation, delivering engineering students the idea to basic systems.
A brief session including the introduction about the RLC resonance circuit placed in series. Also discussed about the mathematical calculations and verification of formula. Circuit diagrams are included as well as the graphs to enhance the better view for the viewer. This is a wholesome package for the engineers at the first stage of their aim.
This informative presentation consists the notes about the solar cell, its working principle, its type and applications. Also there are information about the MPPT, its working and its components. Also the general terms are mentioned in here as well with productive images and graphs. This is a short informative project idle for students aiming engineering.
This creative and informative presentation gives a great gist about the bare codes, types of bar codes, bar code readers and its type. Also for better understanding, there has been provided the ways to decode it for a leman. This presentation also gives an idea about the advantages and disadvantages as well as it applications in different fields. This is well designed presentation for who are aiming for engineering.
This presentation gives a conceptual idea of a graphical algorithm that is Dijkstra's Algorithm. Includes general introduction , the pseudocode, code in form of QR Card, graphical. Also discussing the algorithm in form of graphical images and nodes. Also it include the complexity and application of algorithm in various ranges of fields. This is a fun, eye-catching, conceptual presentation, best suited for students into engineering.
It is a wholesome project for distinguishing the branches of Transition Metal Complex along with its structural formula and its structures. Overall its a conceptual power point for the followers in engineering stream of their 1st year.
This presentation is an collection of abstract images and information regarding the Space Solar Power. Information about its source, retrieval and other necessities are provided with this file. As a whole its a all in one ppt for the designed topic along with graphics.
The ppt describes usage of functions in c language. Showing basic use of function and determining the differences between function call by value and function call by reference using pointer. It also includes valid use in swapping two numbers in c along with different outputs. Overall its a basic note for c language.
Power Series - Legendre Polynomial - Bessel's EquationArijitDhali
The presentation shows types of equations inside every topic along with its general form, generating formula, and other equations like recursion, frobenius, rodrigues etc for calculus. Its an overall explanation in a brief. You are at correct link to get your work done out of this in your engineering maths.
The topic discusses about the types of wave front formation. It constitutes the difference between diffraction and interference along with a comparison chart and graphics. It also states the types of fringes formation and also states differences between constructive and destructive interference.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
3. ABSTRACT
Bivariate Discrete Distributions details the
latest techniques of computer simulation
for the distributions considered. It
contains a general introduction to the
structural properties of discrete
distributions, including generating
functions, moment relationships, and the
basic ideas of generalizing and much
more.
5. INTRODUCTION
In this presentation we will consider two or more random variables defined
on the same sample space and discuss how to model the probability
distribution of the random variables jointly. We will begin with the discrete
case by looking at the joint probability mass function for two discrete
random variables.
6. DISCUSSION
JOINT DISTRIBUTION OF RANDOM BIVARIATES
Let X be a random variable the values
X : x1 x2 x3 ……. xm
Let Y be a random variable assuming the following values corresponding to each xi
Y : y1 y2 y3 ……. Yn
In the table that will be shown in next slide,
There are mn number of values (xi,yj) . These values are known as Bivariate Data.
Also,
Pij = Probability of assuming the pair (xi,yj) by (X,Y)
= P { (xi,yj) }
= P ( X = xi, Y = yj )
are known as Joint Probability Mass of Bivariate (X,Y)
7. BIVARIATE JOINT DISTRIBUTION TABLE
Where the row wise and column wise
total are:
• PXi = pi1 + pi2 + …. + pin = σ𝑗=1
𝑛
𝑝𝑖𝑗
• PYi = p1j + p2j + …. + pmj = σ𝑖=1
𝑚
𝑝𝑖𝑗
The grand total:
• σ𝑖=1
𝑚
𝑝𝑋𝑖 + σ𝑗=1
𝑛
𝑝𝑌𝑗 = σ𝑗=1
𝑛
σ𝑖=1
𝑚
𝑝𝑖𝑗 = 1
8. MARGINAL DISTRIBUTION
This probability distribution of X is called as Marginal Distribution of X
X : x1 x2 x3 …… xm Total
pXi: pX1 pX2 pX3 …… pXm 1
Similarly this probability distribution of Y is called as Marginal Distribution of Y
Y : y1 y2 y3 …… yn Total
pYj: pY1 pY2 pY3 …… pYn 1
The row wise totals PXi and the column wise totals PYi are called Marginal Probability Mass of
X and Y respectively.
9. INDEPENDENT RANDOM VARIABLES
Let (X,Y) be a pair of random variables having joint distribution discussed in previous slide. If
pij = pXi pYj
= P ( X = xi, Y = yj )
= P ( X = xi ) P ( Y = yj )
Hold for all values of i ( 1 ≤ i ≤ m ) and j ( 1 ≤ j ≤ n ) then X and Y are called Independent Random
Variables.
Theorem:
If X and Y are independent random variables and A, B are two events then
P { X ∈ A, Y ∈ B } = P ( X ∈ A ) P ( Y ∈ B )
and vice versa.
10. Problem:
Let (X,Y) be a bivariate having the following joint distribution:
Check whether X and Y are independent or not
Solution:
Here we see every data in the main body of the table is equal
to the product of the corresponding data in last column and
last row, e.g 0.35 = 0.70 x 0.50, 0.06 = 0.30 x 0.20 etc.
ILLUSTRATIVE EXAMPLE 1
That is
P ( X = 0.20, Y = 5 ) = P ( X = 0.20 ) P ( Y = 5),
P ( X = 9, Y = 7 ) = P ( X = 9 ) P ( Y = 7 ) etc.
So, X & Y are independent random variable.
11. Problem:
An urn contains 3 Red, 2 White and 5 Blue balls. Three balls are drawn from the urn. X and Y
denote the number of Red and White balls in a draw. Find the Joint Distribution of (X,Y).
Hence find P ( X ≤ 2, Y ≥ 1 ).
Find the Marginal Distribution of Y and hence find the probability of drawing more
than 1 White balls. Are X and Y independent random variable?
Solution:
Consider X and Y as Probability of Red and White balls.
Take the values of X as 0, 1, 2, 3 and Y as 0, 1, 2.
Create a table with values of the bivariate (X,Y).
Where, P { (xi,yj) } = P ( X = xi, Y = yj )
The corresponding probabilities are:
1) P(0,0) = Probability of “no Red”,”no White”,”3 Blue” = Τ
5
𝐶3 10
𝐶3
= 0.083
ILLUSTRATIVE EXAMPLE 2
12. 2) P(0,1) = Probability of “no Red”,”1 White”,”2 Blue” = Τ
2
𝐶1 ∗5
𝐶2 10
𝐶3
= 0.16
3) P(0,2) = Probability of “no Red”,”2 White”,”1 Blue” = Τ
2
𝐶2 ∗5
𝐶1 10
𝐶3
= 0.041
4) P(1,0) = Probability of “1 Red”,”no White”,”2 Blue” = Τ
3
𝐶1 ∗5
𝐶2 10
𝐶3
= 0.25
5) P(1,1) = Probability of “1 Red”,”1 White”,”1 Blue” = Τ
3
𝐶1 ∗2
𝐶1 ∗5
𝐶1 10
𝐶3
= 0.25
6) P(1,2) = Probability of “1 Red”,”2 White”,”no Blue” = Τ
3
𝐶1 ∗2
𝐶2 10
𝐶3
= 0.025
7) P(2,0) = Probability of “2 Red”,”no White”,”1 Blue” = Τ
3
𝐶2 ∗5
𝐶1 10
𝐶3
= 0.125
8) P(2,1) = Probability of “2 Red”,”1 White”,”no Blue” = Τ
3
𝐶2 ∗2
𝐶1 10
𝐶3
= 0.05
9) P(2,2) = Probability of “2 Red”,”2 White”,”no Blue” = P(ϕ) = 0
10) P(3,0) = Probability of “3 Red”,”no White”,”no Blue” = Τ
3
𝐶3 10
𝐶3
= 0.008
11) P(3,1) = Probability of “3 Red”,”1 White”,”no Blue” = P(ϕ) = 0
12) P(3,2) = Probability of “3 Red”,”2 White”,”no Blue” = P(ϕ) = 0
ILLUSTRATIVE EXAMPLE 2 - CONTINUED
}
13. ∴ The Joint Distribution of (X,Y) is given by:
Now, P (X ≤ 2, Y ≥ 1 )
= P ( 2,1 ) + P ( 2,2 ) + P ( 1,1 ) + P ( 1,2 ) + P ( 0,1 ) + P ( 0,2 )
= 0.05 + 0 + 0.25 + 0.025 + 0.16 + 0.041 = 0.526
The Marginal Distribution of Y is given by
Y : 0 1 2
pYj : 0.466 0.466 0.066
ILLUSTRATIVE EXAMPLE 2 - CONTINUED
Probability of “ more than 1 White balls “:
P ( Y ≥ 1 ) = 0.466 + 0.133 = 0.6
From the above table we see, = 0.083 ≠ 0.284 x 0.466
∴ X, Y are not independent
14. APPLICATIONS
The bivariate distribution is useful in analyzing the relationship between two
randomly distributed variables, and thus has heavy application to biology and
economics where the relationship between approximately-random variables
is of great interest. For instance, one of the earliest uses of the bivariate
distribution was in analyzing the relationship between a father's height and
the height of their eldest son, resolving a question Darwin posed in his book
the “The Origin of Species”.
Also used in measuring systems, such as those used in coordinate measuring
machines (CMMs), laser interferometers, linear or rotary encoders, etc.
15. CONCLUSION
In real life, we are often interested in several random variables
that are related to each other. For example, suppose that we
choose a random family, and we would like to study the number of
people in the family, the household income, the ages of the family
members, etc. Each of these is a random variable, and we suspect
that they are dependent. In this presentation, we developed the
tools to study joint distributions of random variables.
16. REFERENCES
• [1]https://online.stat.psu.edu/stat414/lesson/17/17.1
• [2]https://bookdown.org/compfinezbook/introcompfinr/Bivariate-
Distributions.html
• [3]https://en.wikipedia.org/wiki/Random_variable#Discrete_random
_variable
• [4]https://en.wikipedia.org/wiki/Joint_probability_distribution
• [5]https://www.probabilitycourse.com/chapter5/5_1_0_joint_distribut
ions.php
• [6]https://www.stat.ncsu.edu/people/bloomfield/courses/st380/slide
s/Devore-ch05-sec1-2.pdf
• [7]https://brilliant.org/wiki/multivariate-normal-distribution/
• [8]Page 128 Engineering Mathematics Vol – 2A by B.K.Pal & K.Das,
published by U.N Dhur & Sons Private Ltd.