"OR" or Unions

Mutually Exclusive Events

Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint.

If two events are disjoint, then the probability of them both occurring at the same time is 0.

   Disjoint:  P(A and B) = 0

If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.

Specific Addition Rule

Only valid when the events are mutually exclusive.

   P(A or B) = P(A) + P(B)

Example 1:

Given: P(A) = 0.20, P(B) = 0.70, A and B are disjoint

I like to use what's called a joint probability distribution. (Since disjoint means nothing in common, joint is what they have in common -- so the values that go on the inside portion of the table are the intersections or "and"s of each pair of events). "Marginal" is another word for totals -- it's called marginal because they appear in the margins.

The values in red are given in the problem. The grand total is always 1.00. The rest of the values are obtained by addition and subtraction.

Non-Mutually Exclusive Events

In events which aren't mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.

General Addition Rule

Always valid.

   P(A or B) = P(A) + P(B) - P(A and B)

Example 2:

Given P(A) = 0.20, P(B) = 0.70, P(A and B) = 0.15

Interpreting the table

Certain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.

"AND" or Intersections

Independent Events

Two events are independent if the occurrence of one does not change the probability of the other occurring.

An example would be rolling a 2 on a die and flipping a head on a coin. Rolling the 2 does not affect the probability of flipping the head.

If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring.

Specific Multiplication Rule

Only valid for independent events

   P(A and B) = P(A) * P(B)

Example 3:

P(A) = 0.20, P(B) = 0.70, A and B are independent.

The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.

Dependent Events

If the occurrence of one event does affect the probability of the other occurring, then the events are dependent.

Conditional Probability

The probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A)

General Multiplication Rule

Always works.

   P(A and B) = P(A) * P(B|A)

Example 4:

P(A) = 0.20, P(B) = 0.70, P(B|A) = 0.40

A good way to think of P(B|A) is that 40% of A is B. 40% of the 20% which was in event A is 8%, thus the intersection is 0.08.

Independence Revisited

The following four statements are equivalent

1. A and B are independent events
2. P(A and B) = P(A) * P(B)
3. P(A|B) = P(A)
4. P(B|A) = P(B)

The last two are because if two events are independent, the occurrence of one doesn't change the probability of the occurrence of the other. This means that the probability of B occurring, whether A has happened or not, is simply the probability of B occurring. 

For more information click here:www.math.unb.ca/~knight/webstaty.htm

How to write a Formal Report

1. Title page 

   The title should clearly indicate the subject of the report. The title page should have the title, name or names of the authors, date, and course on a single page.

2. Abstruct

   The object of the abstract is to give the reader enough information to determine if the report should be read. The abstract should be self contained, should be short (100-200words) and should state the following concisely:

   1. What the author has done.
   2. How it was done (if that is important).
   3. The principal results (numerically, when possible).
   4. The significance of the results. See page 13 for example of abstracts.

3. Intrduction

   The introduction orients the reader with respect to the problem. The object is to get the reader knowledgeable enough to understand the following sections. It may include the following:

   1. Background information to establish the motivation for doing the work.
   2. Objective of the work.
   3. Any theory necessary to understand the results presented.

4.  Body of the report

   The body of the report contains the primary message in detail. The writer should communicate information efficiently and effectively to the reader. The body may have several sections or subsections which should have appropriate titles. (Don't call the body "Body.") The following sections could be included:

   1. Procedure. Write a brief account including circuit diagrams where necessary. The lab handout may be referenced (as an Appendix) but should not appear in the body of the report.
   2. Theory/calculations. Include appropriate theory and necessary equations (with references if needed). Methods of calculations should be indicated or sample calculations given.
   3. Results. Present all experimental results. Use visual forms of presentation such as graphs where possible. Figures must be numbered and titled.
   4. Discussion of results. Discuss measurement problems and errors in measurements, calculations, and results. Compare results to theoretical and/or expected results.

5. Conclution.

   Each conclusion should be numbered and clearly stated. Your conclusions could include the following items:

   1. What is shown by this work and its significance.
   2. Limitations and advantages.
   3. Application of results.
   4. Recommendations for further work.

6. Other OptOther optional sections.

   Many reports may include one or more of the following optional sections:

   1. Executive Summary. Often an executive summary is given to summarize the entire report. It may be that this is the only part of the report that is read by an executive. It should briefly summarize the entire report. When included, the executive summary follows the abstract.
   2. Appendices. The appendices contain relevant supporting material which may not be strictly necessary to understanding elements of the report.
   3. References. When information from some other source is used, either as a direct quotation or paraphrased, that source should referenced. Usually, a number in brackets [ ] is inserted in the text and is used to specify the reference citation in the reference section. The references are listed in order of their appearance in the report.
   4. Bibliography. The bibliography includes general reference information about the topic of the report but not specific information referred to in the report.

How to Write a Report

Steps

1. Prepare an outline. Outline what you want to do on a piece of paper. There should be at least:
   • An introduction.
   • Middle sections with headings, detailing your research, ideas and discussion. Keep this at about 3 to 5 different topics--at the most.
   • A summary and/or conclusion. A summary is a retelling of what you have reported on; a conclusion draws together your feelings or arguments about the topic to reach your final point of view.
2. Add a bibliography. Write or type your bibliography (a listing of your report sources) on a piece of paper or if you have a bibliographic page, write it down on that.
3. Write a rough draft. Proofread it and mark your errors clearly. Errors are not only spelling and grammar but also jumbled ideas and missing points.
4. Rewrite your report. Add pictures if you would like to or if it enhances the look. Use colored print if it is appropriate for the report.
5. Print and check for final errors. Bind the report if it is appropriate, or place in a folder.

Tips

• You may need more than two note cards for your research: One for the books and one for the internet.
• To catch errors in your typing easily, read the paper to yourself aloud at home before turning it in.
• Ask someone else to proofread your paper and offer constructive criticism.
• Be sure to rely on more than one source for your information.
• When using information from the internet, make sure it comes from a reputable source. Look on the page and make sure you know who wrote the information and why they are providing it.
• While writing, assume that your reader knows little to nothing about the subject. Add details and definitions to topics in the paper.

Warnings

• Don't delay your research until the last minute. Report creation takes longer than you might think, especially when you start fiddling with color, photos, borders, headings etc and that's only after the information has been written up properly!
• Do not start fiddling with color, photos, borders, headings etc. until the information has been written up properly. If you do, a lot of time can disappear and you will not have time left to write a good report.
• Do not take someone's information for your own.

• You should list the site references the way the site asks people to.

Things You'll Need

• You will need books and some research equipment.
• You will need to know what you are looking for.

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Why conflicts arise
Conditions creating conflict situations
Conflict as a process
Effects of conflicts
Elements of a conflict
Theory of conflict management
Response styles
Dealing with conflict
Ways to resolve conflict
Conflict-resolution behaviour
Strategies for managing conflicts
Conflicts in research organizations
Summing up
References