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#### SCHOOL OF MATHEMATICAL SCIENCES BACHELOR OF SCIENCE (HONS) IN ACTUARIAL STUDIES BACHELOR OF SCIENCE (HONS) IN FINANCIAL ANALYSIS BACHELOR OF SCIENCE (HONS) IN FINANCIAL ECONOMICS BACHELOR OF SCIENCE (HONS) IN INDUSTRIAL STATISTICS ACADEMIC SESSION: MARCH 2020 SEMESTER MAT 204 4 INTRODUCTION TO STATISTICS / MST 2014 MATHEMATICAL STATISTICS I ASSIGNMENT: INDIVIDUAL PROJECT DUE DATE: 3 July 2020 @5 pm INSTRUCTIONS TO CANDIDATES 1

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SCHOOL OF MATHEMATICAL SCIENCES BACHELOR OF SCIENCE (HONS) IN ACTUARIAL STUDIES BACHELOR OF SCIENCE (HONS) IN FINANCIAL ANALYSIS BACHELOR OF SCIENCE (HONS) IN FINANCIAL ECONOMICS BACHELOR OF SCIENCE (HONS) IN INDUSTRIAL STATISTICS ACADEMIC SESSION: MARCH 2020 SEMESTER MAT 204 4 INTRODUCTION TO STATISTICS / MST 2014 MATHEMATICAL STATISTICS I ASSIGNMENT: INDIVIDUAL PROJECT DUE DATE: 3 July 2020 @5 pm INSTRUCTIONS TO CANDIDATES 1. This assignment will contribute s 40% to your final grade . 2. This is an individual project . Answer ALL quesitons. The assignment must be typewritten with double line spacin g 3. Marks will be allocated for correctness and clarity of the work . Use R language for the computational part. Include the R script, solutions and conclusion to you report for each question. Provide your solution carefully and neatly, preferably in complete and grammatically correct sentences. Comment your code with the # sign. Every function should have a comment. 4. Make sure you begin a new page for each question and state the question number clearly. 5. Submit the completed softcopy of your assignment to ELearn , with the following file name: student_ID _#.doc (for example: 17005577. doc). IMPORTANT Assignments must be submitted on their due dates. If an assignment is submitted after its due date, the following penalty will be imposed: ? One to two days late : 20% deducted from the total marks awarded. ? Three to five days late : 40% deducted from the total marks awarded. ? More than five days late : Assignment will not be marked. Question 1 This question is designed to discover the Central Limit Theorem (CLT) and learn to describe the predictable pattern of the generating empirical distributions of sample means. Consider a random sample from the assigned distribution based on your Student ID ’s number (refer to Appendix ). (a) Describe the parameters and the probability density function (pdf) of the random variable. Plot th e density graph of the distirbution. (b) Generate random sample s of size n = 5, n = 50 and n = 100 from the assigned dist ribution . (c) Calculate the sample mean, sample standard deviation from the sample s generated in part (b).

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