MA1259 PROBABILITY AND STATISTICS syllabus

MA1259               PROBABILITY AND STATISTICS                  3  1  0  100

AIM:
The scope of probability and statistics in engineering applications is well known. This course aims at providing the requisite skill to apply the statistical tools in engineering problem.

OBJECTIVES:
At the end of the course, the students would
•    Have a fundamental knowledge of the basic probability concepts.
•    Have a well – founded knowledge of standard distributions which can describe real life phenomena.
•    Acquire skills in handling situations involving more than one random variable and functions of random variables.
•    Be introduced to the notion of sampling distributions and have acquired knowledge of statistical techniques useful in making rational decision in management problems.
•    Be exposed to statistical methods designed to
contribute to the process of making scientific judgments in the face of uncertainty and variation.

UNIT I       PROBABILITY AND RANDOM VARIABLE                9 +3
Axioms of probability - Conditional probability - Total probability - Bayes theorem - Random variable - Probability mass function - Probability density functions - Properties- Moments - Moment generating functions and their properties.

UNIT II      STANDARD DISTRIBUTIONS                        9 +3
Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.

UNIT III    TWO DIMENSIONAL RANDOM VARIABLES                9 + 3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and Regression - Transformation of random variables - Central limit theorem .

UNIT IV    TESTING OF HYPOTHESIS                                          9 + 3
Sampling distributions – Testing of hypothesis for mean, variance, proportions and differences using Normal, t, Chi-square and F distributions - Tests for independence of attributes and Goodness of fit.

UNIT V     DESIGN OF EXPERIMENTS                        9 + 3
Analysis of variance – One way classification – CRD - Two – way classification – RBD - Latin square.

TUTORIAL                                                                                        15

                                                                                              TOTAL : 60
TEXT BOOKS:
1.     Ross. S., “A first Course in Probability”, Fifth Edition, Pearson Education, Delhi 2002. (Chapters 2 to 8)
2.     Johnson. R. A., “Miller & Freund’s Probability and Statistics for Engineers”, Sixth Edition, Pearson Education, Delhi, 2000. (Chapters 7, 8, 9, 12)

REFERENCES:
    1.     Walpole, R. E., Myers, R. H.  Myers R. S. L. and Ye. K, “Probability and     Statistics for     Engineers and Scientists”, Seventh Edition, Pearsons Education,     Delhi , 2002.
    2.      Lipschutz. S and Schiller. J, “Schaum’s outlines - Introduction to Probability and Statistics”,     McGraw-Hill, New Delhi, 1998.
    3.     Gupta, S.C, and Kapur, J.N., “Fundamentals of Mathematical Statistics”, Sultan Chand, Ninth     Edition , New Delhi ,1996.
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