# MTH305 Principles of Applied Probability Assignment Sample

MTH305 Principles of Applied Probability is a substantial course for Singaporean students who aspire to earn knowledge and understanding in the probability area of mathematics. This course is offered at the very eminent and top-leading none other than Singapore University of Social Sciences. SUSS University offers a variety of courses for a wide range of studies. Besides, the majority of the students who wish to go further in their career with a mathematics background generally opt the SUSS MTH305 course.

This course gives a comprehensive knowledge about the concepts, logic, rules, and theorems of the probability as well as make the students capable of solving all the intricate real-life practical problems as well.

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Along with great expertise, the MTH305 SUSS course also provides Singaporean students with different types of assignments. The students have to complete those **university assignments** before a pre-set deadline in order to get good grades for their final mark sheet.

## Major Objectives of Principles of Applied Probability (MTH305) Course

The goal behind introducing the applied probability and its principles to the students is to equip the Singaporean students with a thorough understanding of the probability to make them able to analyze the real-life problems related to chances and possibilities.

MTH305 Principles of Applied Probability is a modular undergraduate course offered to the Singaporean students in order to let them understand the random phenomena and figure out the problem-solving logic and concepts.

## What will the MTH305 Course Teach Singaporean Students?

Our life is full of odds, randomness, and arbitrary situations. Everyone faces some kind of situation which is based on possibilities and everyone takes chances for something on a regular basis.

**There are numerous examples around us that are full of possibilities like-**

- Any scientist taking measurements in the laboratory,
- When a surgeon is studying the heartbeats on the electrocardiogram,
- Buying a lottery ticket with a hope of winning among millions of other candidates like us
- When an economist studies the price fluctuations

The MTH305 SUSS course will teach the students about understanding and solving the problems which consist of some situations related to possibilities and randomness. The Singaporean students will find out how to deal with such phenomena focusing on modeling and problem-solving.

This course describes a practical situation and coaches the students to develop a probability model and describe its features. After that, the model is analyzed mathematically in order to know the possibilities of a situation to occur and all the probabilities associated with it.

## Topics included in the SUSS MTH305 course

There is never any end to studies and the same with the topics in a subject.

**Here are some of the topics which are emphasized in the MTH305 Principles of Applied Probability course: –**

- Probabilities
- Random processes
- The Poisson distribution
- Branching processes
- Random variables
- Random walks
- Markov chain
- Birth processes
- Stochastic processes
- Point and types of point process
- Death processes, etc.

Not only these great topics, but students will also be getting various probability assignments as well. They will have to complete them as these will carry a significant weightage in their final results.

## What is a probability assignment?

The students of Singapore, while pursuing any course program get various kinds of assignments. Similarly, the scholars who are pursuing any educational course in mathematics with principles of probability as a major, get various SUSS MTH305 Principles of Applied Probability assignments on the topics of probability with questions of different complexity levels.

The probability assignments are the set of questions including the entire range of probability like random processes, questions about games, sample spaces, etc.

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## Types of probability

Before solving the probability assignments, one should comprehend the types of problems first.

**There are three types of probabilities: –**

- Theoretical Probability
- Experimental Probability
- Axiomatic Probability

## Formula for probability

**The probability depends on two things that are-**

- Expected outcomes
- Total possible outcomes

So, the formula for probability is-

**Probability= the number of wanted or expected outcomes/ the number of total possible outcomes**

Also, there are many other formulas as well for solving different probability questions which you might study in the SUSS MTH305 Principles of Applied Probability course.

Besides, here is the nCr formula which is one of the most crucial ones in the probability arena as it is one of those which is used on most of the probability problems.

**nCr= n! / r! * (n-r)!**

## Are there any rules in Probability too?

Students’ life is no less than any rule book and more above that they have to study and follow a variety of rules in their studies also. Yes, there are some rules in probability too.

**We can understand those rules by the following points: –**

- For any event A, 0 ≤ P(A) ≤ 1
- The sum of the probabilities of all possible outcomes is 1
- The Complement Rule
- Probabilities Involving Multiple Events- P(A or B) = P(event A occurs or event B occurs or BOTH occur)
- Addition Rule for Disjoint Events- NOT disjoint, P(A and B) ≠ 0, ARE disjoint, P(A and B) = 0
- Finding P(A and B) using Logic- P(A and B)= P(both event A occurs and event B occurs)
- The General Addition Rule- P(A or B) = P(A) + P(B) – P(A and B), etc.

## How can probability be used in statistics?

The statistics can be used while solving any practical yet probability problem. For example, if you want to know the chances of your holiday plane will crash, you will need to find out the stats and see how many planes generally cash in a year.

This way, the probability, and statistics can be used together.

Besides, we can use probability to prognosticate the results of an experiment under assumptions. It can be done by calculating the probabilities of error greater than the given amount as well as the probability of provided departure between the prophecy and the result under the assumption.

## Educational Outcomes of SUSS MTH305 Principles of Applied Probability Course

After studying all such great topics and solving a variety of problems, students ascend with wonderful outcomes.

**These are: –**

- Compute the probability of any type of events
- They can prove any mathematical statement in stochastic processes
- They can solve any general differential equation of some probability function
- Evaluate the reducibility and/or periodicity of a given Markov chain

Now that the student has earned all the essential information and skills to deal with applied probability problems, he also has to complete his assignments on time. Those assignments are not just a part of the course but also a major part of their result.

The **TMA in SUSS**, CMA, quizzes, etc. carries 30% weightage in the final course result and this is why the students need to complete those assignments by the deadline given by their professor.

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