B.Sc. Statistics
3rd Semester Syllabus
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MJC-3 : Numerical Analysis & Sampling Distribution (संख्यात्मक विश्लेषण और नमूनाकरण वितरण)
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Unit 1: UNIT I
◦Finite difference: Different types of operators and their properties
◦Fundamental theorem of finite differences
◦Missing terms (equal intervals)
◦Factorial notation
◦Assumptions and uses of interpolation
◦Gregory Newton's Forward and Backward Interpolation formula for equal intervals
Unit 2: UNIT II
◦Interpolation with arguments at unequal intervals divided differences Δ
◦Theorems on divided differences
◦Newton's divided difference formula
◦Lagrange's interpolation formula
Unit 3: UNIT III
◦Parameter and statistic
◦Sampling distribution of a statistics
◦Standard errors of sample mean
◦Sample variance and sample proportion
◦Null and alternative hypotheses
◦Level of significance
◦Type I and Type II errors and critical region
◦Large sample tests
◦Test of proportion
◦Mean and standard deviation (For one and two-sample)
Unit 4: UNIT IV
◦Exact sampling distribution: Definition and derivation of p.d.f. of χ2, Student's t and Fishers F-distribution, with their mean, variance, m.g.f., and cumulant generating function, additive property and limiting form of χ2, t, F distribution
◦Relationship between them and their applications
Reference Books:
- Gupta, S. C. and Kapoor, V. K. (2020): Fundamentals of Mathematical Statistics, S. Chand & Sons, New Delhi.
- Goon A.M., Gupta M.K. and Dasgupta B. (2002): Fundamentals of Statistics, Vol. I & II, The World Press, Kolkata.
- Saxena, H. C. (2010): Calculus of finite differences, S. Chand & Sons, New Delhi.
- Sastery S.S.(2012): Introductory Methods of Numerical Analysis, Prentice Hall of India