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### MCA10 102 Probability and Statistics

Course Materials
 Prof. C. N. Parvathy Antharjanam This course was first taught by Prof. C.N. Parvathy Antharjanam, Department of Applied Sciences, Vidya Academy of Science & Technology, in the academic year 2010-2011, the year in which the revised syllabi for MCA was implemented in Calicut University.(There was a course with identical title but with code MCA2K 102 in the earlier syllabi. The contents of the two courses MCA2K 102 and MCA10 102 are nearly identical. Prof. Antharjanam had also taught the earlier course.) These course materials were developed under Prof. Antharjanam's direction.

Syllabus

Objectives

This course is objected to inculcate the students an adequate understanding of the basic concepts of probability theory and statistics to make them develop an interest in the area which may find useful to pursue their studies.

MODULE 1: (12 Hrs)

Probability distributions:- Random variables, Binomial distribution, Hyper geometric distribution; Mean and variance of probability distribution, Chebysheve's theorem, Poisson approximation to the Binomial, Poisson processes, Geometric distribution, Normal distribution, Normal approximation to Binomial distribution, Uniform distribution, Log-Normal Distribution, Gamma distribution, Beta distribution, Weibull distribution.

MODULE 2: (10 Hrs)

Sampling Distributions and Inference concerning Means:- Population and Samples, The Sampling distribution of the mean (Sigma known and Sigma unknown), Sampling distribution of variance, Point estimation, Bayesian estimation, Tests of Hypotheses, The null hypotheses and the significance tests, Hypotheses concerning one mean, Operating characteristic curves, Inference concerning two means.

MODULE 3: (10 Hrs)
Inference concerning Variances and Proportions:- Estimation of variances, Hypotheses concerning one variance, Hypothesis concerning two variances, Estimation of proportions, Bayesian estimation, Hypotheses concerning one proportion, Hypotheses concerning several proportions, Analysis of r x c tables, Goodness of fit

MODULE 4: (10 Hrs)
Correlation and regression analysis: Curve fitting, the method of least squares, inference based on the least square estimators, curvilinear regression, correlation, Fisher's transformation, inference concerning correlation coefficient.

MODULE 5: (10 Hrs)
Analysis of Variance:- General principles, Completely randomized designs, Randomized Block diagram, Multiple comparisons, Some further experimental designs, Analysis of co variance.

Text Books
1.    Johnson R A, Miller and Freund’s Probability for Engineers

Reference Books
1.    Levin R I & Rubin DS, Statistics for Management, PHI
2.    J S Milton, Jose C Arnold, Probabilities in Engineering and Computing Science, McGraw Hill
3.    S M Rose, Introduction to Probability and Statistics for Engineers and Scientists, John Wiley
4.    Harry Frank and Steven C, Statistics: Concepts and Application, Cambridge University Press

Sessional work assessment
Assignments 2x10 = 20
Tests2x15 = 30
Total marks = 50

University examination pattern
Seven questions covering all the five modules .Each carries 20 marks and each question should have minimum of two parts. There should be a minimum of one question from each module. There should not be more than 2 questions from any module. The student has to answer any five full questions for scoring full marks.

Old Question Papers

The syllabi of the paper MCA 2K 102 Probability & Statistics (old syllabus) and of the paper MCA10 102 Probability & Statistics (new syllabus) are exactly identical. So University Examination question papers as per the old syllabi could be considered as models for question papers as per the new syllabi.The following question papers are available for reference.