Statistical And Computational Mathematics Assignment - Statistics and Probability

Learning Outcomes

• Critically evaluate statistical applications and others use of statistical evidence.
• Synthesise a range of techniques and apply them within a specified framework.
• Develop programs to solve computationally intense problems.
• Understand problems that are suited to being solved on a computer.

Question 1 - Qualitative Research

(a) Aims and Methods

i. Define a clear software related research aim. List the under-pinning questions that would need to be researched to meet the chosen aim.

ii. Describe a minimum of four methods of collecting qualitative data. For each method, give a generic example of where it would be used, and why.

iii. Critically evaluate two of these methods which would be suitable for your research aim.

(b) Design & Validation

i. Design a short online questionnaire (15 questions) to collect initial data for your research aim.

ii. Design a further set of online interview questions to follow from your questionnaire.

(c) Data Capture & Analysis

i. Using your questionnaire and interview questions, collect 20 questionnaire responses and 5 interview transcripts.

ii. Obtain and analyse feedback, from your respondents about the questionnaire - i.e. layout, ease of answering, etc.; and where appropriate, the interview - i.e. interviewer's approach, questions, etc.

iii. Analyse the results you have obtained from your research and discuss your conclusions.

Question 1 must be done by using hosting services and client and server scripting. So you need to create a website. Your index page includes the answer from sub-question (a) and you need to create links to: designed questionnaire and interview questions and data capture and analysis. All marks will be given for your web application functionality (you need to clearly demonstrate stats and maths formulas). Make sure your web application is easy to navigate. Bear in mind that your website don't have to be pretty (this is not web design module).

Question 2 - Data Analysis

The following snapshot of file storage space consumed by the design department of a medium sized engineering company was collected over two years at the end of each year.

This data was collected by the computer department to allow them to analyse the data for future file storage planning.

The design department typically produces 3-D CAD models, 2-D CAD drawings, specifications, calculations, e-mails, and quality documents.

Analyse the data appropriately. Use suitable statistics, charts, graphs and diagrams to display results in Excel and discuss your findings. What conclusions can be drawn? Comment on possible uses for this data. All calculations and graphs need to be done by using C++ or C# programming language.

Question 3 - Lucas-Lehmer

You are required to produce a program (in any programming language you like) which will use the Lucas-Lehmer method to find all Mersenne primes possible within 10 minutes on a computer.

The program will start with p=3 and will test as many primes as possible.

On the hand in day every student will load their program and all programs will be started at the same time and run for 10 minutes. The program will automatically stop after 10 minutes of running.

Create a program which will check all prime numbers from 3 upwards to see if they are Mersenne primes.

 Include detailed descriptions of algorithms used and testing of the code together with an explanation of the development of the code.

Question 4 - Inverse Kinematics

(a) Create Inverse Kinematics for 2 degrees' program which will draw a square, then draw circle in that square finally draw letter "S" in the circle.

(b) Investigate Kinematics for hexapod leg. Give examples and demonstrate how start and point of hexapod leg could be calculated.

Cite all references using Harvard system of referencing (use ref in the text too!).

You will need to provide evidences: your code, screenshots, etc.