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.
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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