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Theory of Estimation

The document is an examination paper for STA 303: Theory of Estimation, part of the Bachelor of Science in Actuarial Science program at South Eastern Kenya University for the academic year 2018/2019. It includes various questions covering topics such as definitions of statistical terms, properties of estimators, maximum likelihood estimation, and concepts like sufficiency and interval estimation. Candidates are instructed to answer question one and any two additional questions within a two-hour time frame.

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yuri.rennie
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32 views4 pages

Theory of Estimation

The document is an examination paper for STA 303: Theory of Estimation, part of the Bachelor of Science in Actuarial Science program at South Eastern Kenya University for the academic year 2018/2019. It includes various questions covering topics such as definitions of statistical terms, properties of estimators, maximum likelihood estimation, and concepts like sufficiency and interval estimation. Candidates are instructed to answer question one and any two additional questions within a two-hour time frame.

Uploaded by

yuri.rennie
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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STA 303 Theory of estimation

Barchelor of information technology (South Eastern Kenya University)

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SOUTH EASTERN KENYA UNIVERSITY

THIRD YEAR,SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR


OF SCIENCE IN ACTUARIAL SCIENCE

UNIVERSITY EXAMINATONS 2018/2019

STA 303: THEORY OF ESTIMATION

DATE…..……………… TIME 2 HOURS

INSTRUCTIONS TO CANDIDATES

Answer questionONE and any other TWO questions in this paper.

QUESTION ONE (30 MARKS)

(a) Define the terms below as used in statistics. (3 marks)

(i) Parameter

(ii) Statistic

(iii) An estimator

(b) State any three requirements of a good estimator. (3marks)

(c) Proof that the sample mean is an unbiased estimator of population mean. (4marks)

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(d) Differentiate between parametric and non- parametric statistical test in statistics giving

relevant examples. (4 marks)

(e) Let x1,x2 …, xnbe random sample from a poison distribution with parameter λ. Find the

estimator for λ, using any suitable method. (5 marks)

(f) Proof that the sample mean square (S2) is an unbiased estimator of the population variance.

(4 marks)

(g) Explain the concept of UMVUE in estimation. (4marks)

(h) Explain the meaning of the following terms: (3 marks)


(i) Point estimation
(ii) Confidence interval
(iii) Interval estimation

QUESTION TWO (20 marks)

(a) Using a suitable example proof the consistency requirement of a good point
estimator.
(7marks)
(b) Discuss the concept of jointly sufficient in statistics. (7 marks)
(c) Discuss the concept of interval estimation using a relevant example. (6 marks)

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QUESTION THREE (20 marks)

(a) Let x1,x2 …, xnbe a random sample from a Normal distribution. Find the maximum

likelihood estimators of μ and σ (10marks)

(b) Let x1,x2 …, xn be random samples from uniform distribution in [ϴ - ½ , ϴ + ½] Find the

maximum likelihood estimators of ϴ. (10marks)

QUESTION FOUR (20MARKS)

(a) Explain the concept of factorization criterion in estimation. (10 marks)

(b) Using relevant examples discuss the concept of least squares estimation. (10 marks)

QUESTION FIVE (20 marks)

(a) Discuss the concept of sufficiency as used in estimation theory. (5 marks)


(b) Explain the Cramer-Rao inequality. (6 marks)
(c) Let x1,x2 …, xnbe random sample from apoisson distribution Show that;
T= Max(x1, x2 ………xn) is a sufficient statistic for λ. (9 marks)

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