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Subjective Probability, Addition Law for M.E Events, Simple & Compound Events

Superior University Lahore

Sahiwal Campus

Department:	Information Technology
Programme:	B.S(I.T)
Course:	Statistics and Probability
Topic:	Subjective Probability, Addition Law for M.E Events, Simple & Compound Events
Submitted to:	M Zeeshan sarwar
Submitted by:	Prof. Fyaz hussain
Roll no:	028
Date of Submission:	16/11/2015

                              (shanich108@gmail.com)

Subjective Probability

DEFINITION OF 'SUBJECTIVE PROBABILITY'

A probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject's opinions and past experience.

BREAKING DOWN 'SUBJECTIVE PROBABILITY'

Subjective probabilities differ from person to person. Because the probability is subjective, it contains a high degree of personal bias. An example of subjective probability could be asking New York Yankees fans, before the baseball season starts, the chances of New York winning the World Series. While there is no absolute mathematical proof behind the answer to the example, fans might still reply in actual percentage terms, such as the Yankees having a 25% chance of winning the world series.

(Read more: Subjective Probability Definition | Investopedia http://www.investopedia.com/terms/s/subjective_probability.asp#ixzz3rWsATVJu )

 

 

Addition Law for Mutually Exclusive Events

 

First go through the mutually exclusive events. These are the two or more than two events that have nothing in common. Theorem for Addition law of mutually exclusive events states that:

If there are two events say “x” and “y” and both are mutually exclusive events, then the probability that either “x” or “y” occur is the sum of the probabilities of both the events.

Suppose there are two events named as “x” and “y”, both events have nothing in common. Addition of such event is done by following the addition law for mutually exclusive events.

P(x or y) = p(x u y) = p(x) + p(y)

 

Let make it clear by solving simple examples.

EXAMPLE 1:

A single card is selected from a deck of 52 cards. Find the probability that the randomly selected card is either king or queen.

Solution:

Total number of outcomes = 52

Probability of each single card = 1/52

Now let first find the probability of queen

Probability of queen is represented by = P(Q)

There are four queens in a deck of playing cards.

Therefore, probability of queen = P(Q) = 4/52

Now, let find the probability of king

Probability of king is represented by = P(k)

In the same manner there are four kings in a deck of 52 playing cards.

Therefore, probability of queen = P(K) = 4/52

Addition law of mutually exclusive event is used, as the requirement is to find the probability of king or queen.

Therefore,

P(K or Q) = P(K u Q) = P(K) + P(Q) = 4/52 + 4/52 = 8/52

 

EXAMPLE 2:

A dice is thrown. Find the probability that the face is less than three or it is multiple of 5.

Solution:

When a dice is rolled, there are six possible outcomes

Sample space = S = {1, 2, 3, 4, 5, 6}

Let first find the probability of face that are less than 3.

A = {1, 2} = 2/6

Now second part is that the face is multiple of 5.

B = {5} = 1/6

Use addition law, as again there is nothing in common between the two events.

P (A or B) = P(A u B) = P(A) + P(B) = {1, 2} + {5} = {1, 2, 5}

P(A or B) = 2/6 + 1/6 = 1/2

Definition Of Equally Likely

The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal.

Example of Equally Likely:

·         When you toss a fair coin, you are equally likely to get a head or a tail.

·         When you roll a fair die, you are equally likely to roll a 1, 2, 3, 4, 5, or 6.

Ques: Which one of the following best replaces the blank? 'A and B are playing tennis. The event of A or B winning the match is ______________.'

Choices:

A. a likely event 
B. an unlikely event
C. an equally likely event 
D. none of the above
Correct Answer: C

Solution:

Step 1: Both A and B have equal chances of winning the match.
Step 2: So, it is an equally likely event.

EVENTS

Event is the subset of the sample space or event can also be defined as the collection of either one or more than one outcomes of an experiment. It is sum of all possible outcomes of an experiment. Sample space forms after combining all the events.  Any part of the sample space can be named as an event. Event may be of one outcome or a combination of more than one outcome.

Event with a single outcome is named as simple event and an event with having two or more than two outcomes is known as compound event.

SIMPLE EVENTS:

Simple events can be defined as the single outcome of the performed experiment or it is an event which cannot be broken down any more.

COMPOUND EVENTS:

Compound events are the combination of two or more than two simple event. It can also be defined as an event that contains more than one sample points in it.

EVENT EXAMPLES:

1.     If a single face is considered when a die is rolled, then it will be simple event. For example suppose getting 5 or 6 or 3 or 2 etc… on the die when it is thrown, is called as simple event. If the event is any even number on the die, then the event is consist of points {2, 4, 6}, which is known as compound event. That compound event is consisting of three simple events i.e., {2}, {4} and {6}.

2.     Suppose two dice are rolled simultaneously, then the pair (1, 1) will be the simple event. This is so, because it is a single outcome in the sample space. If event consists of the sum of two dice is ‘’5’’ than it consists of four outcomes i.e., (1, 4), (2, 3), (3, 2), (4, 1) and this is considered to be a compound event.

3.     Suppose two coins are tossed simultaneously, then the pair (HT) will be the simple event. If condition is defined that an event should consist of at least one head then there are three outcomes. These outcomes are (HH), (HT) and (TH) and this is said to be as compound event. That compound event consists of three simple events i.e., {HH}, {HT} and {TH}.

NUMERICALS...

Q#1:

A Marble drawn At Random From a box containing 10 red, 30 white, 20 blue and 15 orange marbles. Find the probability that is:

Ø      Orange or Red

Ø      Not Red or Blue

Ø      Not Blue

Ø      White

Ø      Red, White or Blue

                

SOLUTION:

RED=10               P (RED) =10/75

WHITE=30         P (WHITE) =30/75

BLUE=20            P (BLUE) =20/75

ORANGE=15      P (ORANGE) =15/75

TOTAL=75

Ø  Orange Or Red

P (Orange Or Red) = P (Orange)+ P(Red)

                                  15/75+10/75=25/75=1/3

Ø  Not Red Or Blue

P (Not Red Or Blue) = P (White) +P (Orange)

                                      30/75+15/75=45/75=3/5

Ø  Not Blue

P (Not Blue)= P(White)+P(Red)+P(Orange)

                          30/75+10/75+15/75+15/75=11/15

Ø  White

P (White) =30/75

Ø  Red, White Or Blue

P (Red, White Or Blue) =P(Red)+P(White)+P(Blue)

                                         10/75+30/75+20/75=60/75

Q#2

Of 12 eggs in a refrigerator, 2 are bad. From these, 4 eggs are chosen at random to make cake. What are probabilities that:

Ø      Exactly one is bad

Ø      At least one is bad

SOLUTION:

Total eggs= 12

Bad eggs= 2

Good eggs= 10

n=4

P (exactly 1 bad egg) = 2C1 10C3/12C4=0.48

P (at least one is bad) = 2C1 10C3 + 2C2 10C2/12C4 =0.575

Q#3

A bag contains 14 identical balls, 4 of which are red, 5 black and 5 white. Six balls are drawn from the bag. Find the probability that

Ø      3 are red

Ø      At least two are white

SOLUTION:

N = 14

Red = 4

Black = 5

White = 5

n = 6

P (three are red) = 4C3+ 10C3/14C6= 124/3003=0.041

P (at least two are white) = 5C2. 9C4+ 5C3.9C3+ 5C4. 9C2+ 5C5.9C1/ 14C6= 2289/3003=0.7

SDLC OF SOCIAL MEDIA

Superior University Lahore

Sahiwal Campus

Department:	INFORMATION TECHNOLOGY
Programme:	4 YEAR
Course:	BS-IT
Topic:	SDLC OF SOCIAL MEDIA
Submitted to:	SIR SALEEM
Submitted by:	FAIZAN JAMEEL
	{For More Help shanich108@gmail.com}

                              

ACKNOWLEDGEMENT

 I am very grateful for the strong support and guidance provided to me by my Fundamental Of  IT (FIT) Teacher SIR Muhammad Saleem, Who helped me for good knowledge about my topic also help me in preparing this project I am very thankful to him.

TABLE CONTENTS

NO	TOPIC	PAGE NO
1	System Development life cycle	5
2	Social Networking	6
3	Planning	7
4	Analyses	9
5	Design	10
6	Implementation	11
7	Testing	12
8	Maintenance	13

SUMMARY

My topic is (system development life cycle of social media networking  so I am discussing about  System Development Life Cycle)-SDLC OF social media .The purpose of the Systems Development Life Cycle (SDLC) Standards is to describe the minimum required phases and considerations for developing and/or implementing new systems at the social media.

THE LIFE CYCLE OF A

“SOCIAL NETWORKing”

“System Development Life Cycle”

SDLC stands for System Development Life Cycle or Software Development Life Cycle. It is used to describe functional systems development activity, to gain control of the complexities of systems development, and to ensure the needs of customers and users are the basis for technical activity. The SDLC has made a great impact on developing information systems as a general approach. Adhering to a SDLC increases efficiency and accuracy and reduces the risk of product failure

The System Development Life Cycle (SDLC) is a series of six steps.

ü Planning

ü Analyze

ü Design

ü Implement

ü Testing

ü Maintenance

“Social Networking”

{For More Help shanich108@gmail.com}

Social networking, the art of meeting and building contacts on the Web, is an increasingly popular way to gain personal and professional contacts, make new friends, develop professional relationships, promote personal or business Web sites, and even find a new job. Over the past few years, social networking sites (SNS) have received growing media attention. At many high schools and colleges, every student has a profile on at least one of the SNS such as MySpace and Face book.

Social networking sites have become increasingly versatile. They are not limited to messaging, communicating and displaying networks. Nearly all sites allow users to post photos, videos and often music on their profiles and share them with others. Beyond these, users can even keep up with favorite bands and add applications such as games, quizzes and virtual gift giving.

Every product or service has a product life cycle, and despite the popularity of social networking in this day and age, even social network sites have a product life cycle scenario. Thinking about it in a different way, humans also have a life cycle beginning at birth and ending at death. They go through infancy, growth, maturity, and death. Likewise, social networking is also subject to several stages of its own life cycle.

“Phases of Social networking life cycle”

The phases of Social networking are the following on which the networking sites starts and ends their cycle.

  The phase is depends on:

ü Planning

ü Analyze

ü Design

ü Implement

ü Testing

ü Maintenance

“Planning”

In this case, the system investigation studies one step further. It attempts to find out “What is the problem, and is it worth solving”. The fact that the system investigation looks for is mainly about “defining the requirements” or in other words requirements specification. The initial work of the requirements specification then refers to recognition of the goal of the system and the problems that exist within the current system.

          With opening their API (Application Program Interface) to third-party developers, social networking sites have become the world’s largest application platforms with hundreds of millions monthly users. According to a site comparison among the three biggest SNSs (Compete 2009), as of August 2009, there were 122 million visitors surfing Facebook, 56 million using MySpace and 24 million visiting Twitter. From a business point of view, such a big amount of users stands for uncountable challenges and opportunities. Dramatically, those application developers turn into entrepreneurs on the battle of social networking site platforms. Thus, the first-task for the potential “entrepreneur” is to identify, explo and then select an attractive business opportunity. An attractive and excellent project idea which an entrepreneur searches for and accepts such idea as a basis for his investment decision. Back to the developers’ side, an opportunity might imply a good idea for developing a certain application which has a potential user demand and is deserve to invest money or time to achieve it.

      To gain the information effectively, it is necessary to have a lot of skills involved in and use some of the above mentioned approaches. Sometimes, a couple of similar systems implemented elsewhere which may share invaluable experiences are possible to be found out. Finally, the information collected during this stage will be useful for the next stage of the SDLC.

“Analyses”

                      Systems analysis stage is the phase that establishes the need for and the extent of an information system. This stage attempts to answer the question “What must the information system do to solve the problem”, it involves studying existing systems and work practices to identify strengths, weaknesses and opportunities for improvement.

The systems analysis stage also includes the creation of a logical system design which will be based partly on information collected during the systems investigation stage and partly on new information gathered from the current system. For the sake of creating a logical design, some process techniques might be used such as data flow diagrams (DFDs), hierarchical input process output (HIPO) diagrams, and entity-relationship diagrams (ERDs) However, it must specify the appropriate conceptual data model, inputs, processes and expected output requirements.

In a case that a database is needed for the new application, data-modeling activities or data analysis may also take place in this stage to clarify all entities, together with their attributes, and the relationships among the entities within the database.

“Design”

Once the output of the systems analysis states that a new system will be worth having, designing the new system can be started. Systems design seeks to answer the question “How will the information system do what it must do to obtain the problem solution”. The purpose of this stage is to design a system, a site or an application that fulfills the requirements determined in the analysis stage. The primary output of systems design is a physical design model that either describes the new system or describes how the existing systems will be modified.

          There are a number of ways to incorporate the logical designed model that is generated in the previous stage into a physical design model. For example, to implement the data stores as a series of files, to incorporate some of the data flow diagram processes into a computer system and remain the rest manual, and of those to be computerized, which are to be processed online and which are to be run only offline.

          Even point out that systems design not only details inputs, processes and outputs, but also details user interfaces, specifies hardware, software, database, telecommunications, personnel, procedure components and shows how these components are related.

Likewise, list the details that the systems design documentation should contain: • What is the input data and how the data is inputted into the system?

 • What is the output data?

•What are the processes that converting the input data to output data?

• Structure of the computer and manual files?

• Security issues and back-up provisions?

• Plan for system implementation and testing by the end of this stage, system analysts will?

“Implementation”

The implementation of the new system is led by various procedures followed by the previous stage. It involves creating or acquiring the various system components detailed in the systems design, assembling them, and placing the new or modified system into operation. Based on the physical design model, if it includes computer programs, these have to be written and tested individually, and if it requires hardware and software systems, those also need to be purchased and installed.

It is important that the system is formally tested and accepted before changeover. By contrast, failure will cause a lack of confidence and, possibly, future computer applications. Unlike the previous stages, instead of system analysts, computer programmers are involved in this approach to carry out the design and coding of the program .Particular attention will be paid to security features surrounding the conversion of existing files, whether manual or computer-based, to the new system.

In addition, the database or file structure is created and historical data from the old system, manual or computer-based, is loaded. An important task during implementation is to train the users. Without thorough training, users will be unfamiliar with the new system and unlikely to cope with the new approach, especially with the radical new system. Once all those mentioned above have been done, the new system can be operated and the old system can be discontinued. There could be problems associated with the new system, direct conversion is usually too risky an approach to changeover. After the system becomes fully operational, the next stage of the SDLC will start.

“Testing”

During this phase of the life cycle process, companies have a chance to find any errors, inconsistencies, and vulnerabilities in the software. The organization should have a series of testing procedures and documentation in place so that everyone involved in the project will know their responsibilities, errors are properly documented, and all issues are prioritized and resolved before the software is implemented.

However there are certain criteria for a good server of SNS (Social networking Sites) applications. The considerable factors of choosing a server are the reliability, cost and the most important, whether it is compatible with the SNSs or not.

Once being put on the good server, the application needs a thorough testing before it is formally published to the end users. Scenarios are a good way for testing since they enable users to look at the features and functions offered by a system so that it can reveal problem areas and errors.

“Maintenance”

The final stage of the system development process occurs when the system is running and in continuous use. There will be a review of the system to ensure that it does conform to the requirements set out at the feasibility study stage, and the costs have not exceeded those predicted. This process includes a periodic review or audit of a system, the audit occurs in addition to continually monitoring a new system for potential problems or necessary changes. It is customary to produce an evaluation report to gain an improvement in the way other systems are developed through the process of organizational learning. Shortcomings will be identified, if these are easily rectified, then changes will be made during normal maintenance.

                After the application is published for some time, a review of the application and maintenance is necessary to be conducted to ensure the application does conform to the expectations laid out in the feasibility study and the continued efficient running of the application.

                      The last step of SDLC is to finalize the applications so that they are ready to be used by the users. Different from the traditional SDLC, the publication is specially added in the last stage of the life cycle in order to highlight its importance and specialty. Although the applications are developed for the SNS platform, it does not offer any biding servers to run the application. Therefore the developers in some case need to look for reliable third-party servers to host the implemented applications. There are a large number of good servers.