**MA1253 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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