Probability Distributions

Paper Code: 
STT-123
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course lays the foundation of probability distributions and sampling distributions, their application which forms the basis of Statistical Inference.

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

 

 

 

 

 

STT123

Probability Distributions

(Theory)

 

 

 

 

 

 

The students will be able to –

 

CO11: Identify the behavior of the population and sample and their distribution.

CO12: Able to derive the probability distributions function of random variables and use these techniques to generate data from various distributions.

CO13: Analyse the behaviour of the data by Fitting the discrete and continuous distributions.

CO14: Able to translate real-world problems into probability distributions.

 

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

15.00

Bernoulli distribution, Binomial distribution (compound and truncated also), Poisson distribution (compound and truncated also)- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions

 

15.00

Geometric distribution, Negative Binomial distribution, Hyper-geometric distributions, Power Series distribution- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions

 

15.00

Rectangular distribution, Normal distribution (truncated also), Exponential distribution, Lognormal distribution, Multinomial of binomial and Poisson- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions

 

15.00

Triangular distribution, Gamma distribution (one and two parameter) , Beta distribution( I kind and II kind)  Cauchy distribution (truncated also), Laplace distributions, Pearson’s distribution (Type I, IV and VI)

 

15.00

Chi-Square, t and F distributions (central and non-central) and their applications. Large sample test. Fisher’s Z distributions and their applications. Order statistics: their distributions and properties; joint and marginal distributions of order statistics, sampling distributions of range and median of univariate population.

 

Essential Readings: 

BOOKS RECOMMENDED

 

  • Goon, Gupta & Das Gupta. (2003): Outline of Statistical Theory. Vol. I, World Press.
  • Hogg, R.V. and Craig, A.T.(2009): Introduction to Mathematical Statistics, McMillan.
  • Johnson, S. and Kotz. (1972): Distribution in Statistics, Vol.I, II. And III, Houghton and Muffin.
  • Kendall, M.G. and Stuart. (1996): An Advanced Theory of Statistics, Vol. I,II. Charls Griffin.
  • Mood, A.M., Graybill, F.A. and Boes, D.C.(2007): Introduction to the Theory of Statistics, McGraw Hill, third edition.
  • Mukhopadhyay, P. (1996): Mathematical Statistics, New Central Book Agency (P) Ltd.
  • Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, third edition.

 

 

Academic Year: 
2020-2021
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