- Probability review.
- Conditional Expectation.
- Theorems of total expectation and total variance with proofs and application.
- Transformation of random variables.
- Change-of-variable.
- Moment generating function and Distribution function techniques.
- Order statistic and the sampling distributions of the smallest the largest, k’th order statistics.
- Range, midrange, median, and pair of i’th and j’th order statistics.
- Characteristic function.
- Inversion theorems for continuous and discrete random variables with proofs and application.
- Non-central Chi-square, t and F distributions with application and properties.
- Pearsonian system of distributions,
- Sampling distribution of extreme values.

- Introduction to mathematical statisticsby Hogg, Robert V. | Joeseph McKean | Allen T. Craig

Published by : Dorling Kindersley Pvt. Ltd (New Delhi)

ISBN: 9789332519114.

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- Probability Theory : The Logic of Scienceby Jaynes, E. T.

Publisher: Cambridge University Press

ISBN: 9781139146722 - Probability : With Applications and Rby Dobrow, Robert P.

Publisher: John Wiley & Sons

ISBN: 9781118589359 - Mathematics As a Science of Patternsby Resnik, Michael D.

Publisher: Clarendon Press

ISBN: 9780191519000 - Guide to Teaching Statistics : Innovations and Best Practicesby Woolf, Linda M.

Hulsizer, Michael R