Unit Syllabus: RANDOM VARIABLES

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LESSON PLAN LP-CH - MA2263 Sub Code & Name: MA2263 PROBABILITY AND LP Rev. No: 00 STATISTICS Date: 8.12.2010

Unit: I Branch(Student): CH&BT Semester : IV Page 1 of 6

Unit syllabus: RANDOM VARIABLES Discrete and continuous random variables - Properties- Moments - Moment generating functions and their properties. Binomial, Poisson ,Geometric, Negative binomial, Uniform, Exponential, Gamma, and Weibull distributions Objective: At the end of the unit, the students would  Have a fundamental knowledge of the concept of random variables.  Have a well – founded knowledge of standard distributions which can describe real life phenomena.

Session Teaching Topics to be covered Time Ref No Method 1. Introduction to unit I. Random variables. 50m 2. Probability mass function, probability density function 50m Cumulative distribution function and their properties. 3. Moments and problems based on moments. 50m 4. Moment generating functions (MGF), Properties of Moment 50m generating functions and problems based on MGF. 5. Binomial distribution. 50m 6. Black Poisson distribution. 50m Board 1&5 7. and Geometric distribution and Negative binomial distribution. 50m Chalk 8. Uniform distribution. 50m 9. Exponential distribution. 50m 10. Gamma distribution. 50m 11. Weibull distribution. 50m 12. Summarizing the unit. 50m

1 LESSON PLAN LP-CH - MA2263 Sub Code & Name: MA2263 PROBABILITY AND LP Rev. No: 00 STATISTICS Date: 8.12.2010

Unit: II Branch(Student): CH&BT Semester : IV Page 2 of 6

Unit syllabus: TWO DIMENSIONAL RANDOM VARIABLES Joint distributions - Marginal and conditional distributions – Covariance - Correlation and Regression – function of a random variable-Transformation of random variables - Central limit theorem.

Objective: At the end of the unit, the students would acquire skills in handling situations involving more than one random variable and functions of random variables.

Session Teaching Topics to be covered Time Ref No Method 13. Introduction - Unit Syllabus - Joint distributions. 50m Black 14. 1&5 Board Marginal and conditional distributions. 50m and 15. Chalk Problems on Marginal and conditional distributions. 50m 16. CAT – I 75m 17. Covariance. 50m 18. Properties and problems on Correlation coefficients. 50m 19. Properties and problems on Regression. 50m 20. Black Problems on function of a random variable. 75m Board 1&5 21. and Problems on transformation of random variables. 50m Chalk 22. Central limit theorem. 50m 23. Problems on Central limit theorem. 50m 24. Summarization of Unit-II. 50m

2 LESSON PLAN LP-CH - MA2263 LP Rev. No: 00 Sub Code & Name: MA2263 PROBABILITY AND STATISTICS Date: 8.12.2010

Unit: III Branch(Student): CH&BT Semester : IV Page 3 of 6

Unit syllabus: TESTING OF HYPOTHESIS 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.

Objective: At the end of the unit, the students would be introduced to the notion of sampling distributions and have acquired knowledge of statistical techniques useful in making rational decision in management problems.

Session Teaching Topics to be covered Time Ref No Method 25. Introduction to sampling. 50m 26. Testing of hypothesis for mean using Normal distribution. 50m 27. Testing of hypothesis for differences of mean using Normal 50m distribution. 28. Testing of hypothesis for mean using t-distribution. 50m 29. Testing of hypothesis for differences of mean using 50m t-distribution. Black 30. Board Testing of Hypothesis for proportions. 50m 2&5 and 31. Chalk F-test between variances. 50m 32. Tutorial class. 50m 33. Tests for independence of attributes. 50m 34. Test for goodness of fit. 50m 35. Summarizing the unit. 50m 36. CAT – II 75m

3 LESSON PLAN LP-CH- MA2263 Sub Code & Name: MA2263 PROBABILITY AND LP Rev. No: 00 STATISTICS Date: 8.12.2010 Unit: IV Branch(Student): CH&BT Semester : IV Page 4 of 6

Unit syllabus: DESIGN OF EXPERIMENTS Analysis of variance – One way classification – CRD - Two – way classification – RBD - Latin square.

Objective: At the end of the unit, the students would be exposed to statistical methods designed to contribute to the process of making scientific judgments in the face of uncertainty and variation.

Session Teaching Topics to be covered Time Ref No Method 37. Introduction—Unit syllabus. 50m 38. Analysis of variance. 50m 39. Problems. 50m 40. One-way classification. 50m 41. Problems. 50m 42. Black Tutorial Class. 50m Board 2&5 43. and Completely randomized design. 50m Chalk 44. Problems. 50m 45. Two-way classification. 50m 46. Randomized block design. 50m 47. Latin square. 50m 48. Summarizing the unit. 50m

4 LESSON PLAN LP-CH - MA2263 Sub Code & Name: MA2263 PROBABILITY AND LP Rev. No: 00 STATISTICS Date: 8.12.2010

Unit: V Branch(Student): CH&BT Semester : IV Page 5 of 6

Unit syllabus: RELIABILTY AND QUALITY CONTROL Concepts of reliability-hazard functions-Reliability of series and parallel systems- control charts for measurements (x and R charts) – control charts for attributes (p, c and np charts).

Objective: To know the concepts of Reliability and Quality control.

Session Teaching Topics to be covered Time Ref No Method 49. Introduction—Unit syllabus and Reliability. 50m 50. Concepts of reliability. 50m 51. Hazard functions. 50m 52. Reliability of series and parallel systems. 50m 53. Problems on reliability of series and parallel systems. 50m Black 54. Board Control charts for measurements - x charts. 50m 2&5 and 55. Chalk Control charts for measurements - R charts. 50m 56. Control charts for attributes- p charts. 50m 57. Control charts for attributes - c charts. 50m 58. Control charts for attributes - np charts. 50m 59. Summarizing the unit. 50m 60. CAT – III 75m

LESSON PLAN LP- CH - MA2263

5 Sub Code & Name: MA2263 PROBABILITY AND LP Rev. No: 00 STATISTICS Date: 8.12.2010 Branch(Student): CH&BT Semester : IV Page 6 of 6

Course Delivery Plan:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week I II I II I II I II I II I II I II I II I II I II I II I II I II I II I II C C C

A A A T T T - - - I I I

Units I I I

BOOKS FOR REFERENCES:

1. J. S. Milton and J.C. Arnold, “Introduction to Probability and Statistics”, Tata McGraw Hill, 4th edition, 2007. (For units 1 and 2) 2. R.A. Johnson and C.B. Gupta, “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 7th edition, (2007) 3. 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. 4. Navidi, W, “Statistics for Engineers and Scientists”, Special Indian Edition, Tata McGraw- Hill Publishing Company Ltd, New Delhi,2008. 5. Spiegel, M.R, Schiller, J and Alu Srinivasan, R, “Schaum’s Outlines Probability and Statistics”, Tata McGraw-Hill Publishing Company Ltd. New Delhi ,2007.

Prepared by Approved by

Signature

Name M RADHAKRISHNAN Dr R MUTHUCUMARASWAMY Professor & Head Designation Assistant Professor Department of Applied Mathematics Date 08.12.2010 08.12.2010