SOLUTION: BTEC Higher National Diploma (HND) in Computing

HND Assignment BriefSession: February 2021Programme titleBTEC Higher National Diploma (HND) in ComputingUnit number and title11Maths for Computing (L4)Assignment number & title1 of 1Maths for Computing (L4)Unit Leader–Assessor (s)Amjad AlamIssue Date25/02/2021Final assignmentsubmission deadline07 – 12 June 2021Late submission deadline14 – 19 June 2021The learners are required to follow the strict deadline set by the Collegefor submissions of assignments in accordance with the BTEC level 4 – 7submission guidelines and College policy on submissions.Resubmission deadlineTBAFeedbackFormative feedback will be available in class during the semester.Final feedback will be available within 2 – 3 weeks of the assignmentsubmission date. GeneralGuidelines• The work you submit must be in your own words. If you use a quote or anillustration from somewhere you must give the source.• Include a list of references at the end of your document. You must give allyour sources of information.• Make sure your work is clearly presented and that you use readilyunderstandable English.• Wherever possible use a word processor and its “spell-checker”. Internal verifierReza JoadatSignature (IV of thebrief) *JoadatDate22/02/2021 Department of Information Technology Page 2 of 8 ICON College of Technology and ManagementBTEC HND in ComputingUnit 11: Maths for Computing (L4)Session: February 2021Coursework You are strongly advised to read “Preparation guidelines of the Coursework Document”before answering your assignment.ASSIGNMENTAim & ObjectiveThis assignment is designed so that it enables the student to demonstrate their understanding ofthe mathematical concepts covered in the module through answering various practical problems;divided into four part. The coursework should be submitted as one document in a report format infinal submission.Part 1Number theoryThe GCD (greatest common divisor), LCM (lowest common multiple) and prime numbers is usedfor a variety of applications in number theory, particularly in modular arithmetic and thus encryptionalgorithms such as RSA. It is also used for simpler applications, such as simplifying fractions. Thismakes the GCD, LCM and prime numbers a rather fundamental concept to number theory, and assuch several algorithms have been discovered to efficiently compute it. Primes are the set of allnumbers that can only be equally divided by 1 and themselves, with no other even divisionpossible. Numbers like 2, 3, 5, 7, and 11 are all prime numbers.Demonstrate the concepts of greatest common divisor and least common multiple of a given pair ofnumbers with an example. To support the evidence of your understanding on LCM and GCD, youshould present with pseudocode and a computer program in python to compute LCM and GCDbased on user’s input. It is desirable, to support your findings by identifying multiplicative inversesin modular arithmetic with an example. Produce a detailed written explanation of the importanceand application of prime numbers in RSA encryption (Rivest–Shamir–Adleman). To support theevidence of your understanding on the use of prime numbers, you are required to develop acomputer program in C/ C++ or python to demonstrate the asymmetric cryptography algorithm.Sequences and SeriesArithmetic progressions are used in simulation engineering and in the reproductive cycle ofbacteria. Some uses of AP’s in daily life include uniform increase in the speed at regular intervals,completing patterns of objects, calculating simple interest, speed of an aircraft, increase ordecrease in the costs of goods, sales and production and so on. Geometric progressions (GP’s)are used in compound interest and the range of speeds on a drilling machine. In fact, GP’s areused throughout mathematics, and they have many important applications in physics, engineering,biology, economics, computer science, queuing theory and finance.To support the evidence of your understanding on AP and GP, solve the following 4 problems.1. The cost of borewell drilling cost per feet is £500 for first feet and rises by £100 for eachsubsequent foot. Find the charge when good water found after digging borewell about 161feet.Department of Information Technology Page 3 of 82. The nth term of sequence of number is an = n3 – 6n2 + 11n – 6. Then find the sum of the firstfour terms of that sequence.3. The 6th term of a G.P. is 32 and its 8th term is 128, then find the common ratio of the G.P.4. Find the general expression for sum of the series 6 + 66 + 666 + ……….up to n terms. If n=5,find the actual sum.Part2Probability theory and probability distributionsThe probability of something to happen is the likelihood or a chance of it happening. Values ofprobability lie between 0 and 1, where 0 represents an absolute impossibility and 1 represent anabsolute certainty. The probability of an event happening usually lies somewhere between thesetwo extreme values and it is expressed either as a proper a decimal fraction.1. To support the evidence of your understanding on probability theory and probability distributions,solve the following problems.a. What is the probability of getting a sum of 8 when two dice are thrown?b. Tickets numbered 1 to 15 are mixed up and then a ticket is drawn at random. What is theprobability that the ticket drawn has a number which is a multiple of 3 or 5?c. From a pack of cards, two cards are drawn at random. Find the probability that each card isfrom different suit.d. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random fromthe bag. What is the probability that?i) all of them are red.ii) two is red and the third is blue.e. A survey found that 70% of British victims of health care fraud are senior citizens. If 10victims are selected at random, find(i) the mean number of victims who are senior citizens.(ii) the probability that exactly 3 victims are senior citizens.(iii) the probability that at most 6 victims are senior citizens.(iv) the probability that all but one victim are senior citizensf. X is a normally distributed variable with mean μ = 30 and standard deviation σ = 4. Finda) P (x 21)c) P (30