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AL-302 · Introduction to Probability and Statistics/Official Syllabus

Introduction to Probability and Statistics (AL-302) - Official Syllabus

1
Unit 1

Basic Probability

  • Probability spaces
  • conditional probability
  • independence
  • Discrete random variables
  • Independent random variables
  • the multinomial distribution
  • Poisson approximation to the binomial distribution
  • infinite sequences of Bernoulli trials
  • sums of independent random variables
  • Expectation of Discrete Random Variables
  • Moments
  • Variance of a sum
  • Correlation coefficient
  • Chebyshev's Inequality
2
Unit 2

Continuous Probability Distributions

  • Continuous random varibales and their properties
  • distribution functions and densities
  • normal, exponential and gamma densities
3
Unit 3

Bivariate Distributions

  • Bivariate distributions and their properties
  • distribution of sums and quotients
  • conditional densities
  • Bayes' rule
4
Unit 4

Basic Statistics

  • Measures of Central tendency: Moments, skewness and Kurtosis
  • Probability distributions: Binomial, Poisson and Normal
  • evaluation of statistical parameters for these three distributions
  • Correlation and regression
  • Rank correlation
5
Unit 5

Applied Statistics

  • Curve fitting by the method of least squares
  • fitting of straight lines, second degree parabolas and more general curves
  • Test of significance: Large sample test for single proportion
  • difference of proportions
  • single mean
  • difference of means
  • difference of standard deviations
6
Unit 6

Small samples

  • Test for single mean
  • difference of means and correlation coefficients
  • test for ratio of variances
  • Chi-square test for goodness of fit and independence of attributes

Reference Books

  • Advanced Engineering Mathematics — Erwin Kreyszig — John Wiley & Sons — 9th Edition
  • Introduction to Probability Theory — P. G. Hoel, S. C. Port, C. J. Stone — Universal Book Stall — Reprint
  • A First Course in Probability — S. Ross — Pearson Education India — 6th Ed.
  • An Introduction to Probability Theory and its Applications, Vol. 1 — W. Feller — Wiley — 3rd Ed.
  • A text book of Engineering Mathematics — N.P. Bali, Manish Goyal — Laxmi Publications — Reprint
  • Higher Engineering Mathematics — B.S. Grewal — Khanna Publishers — 35th Edition
  • Engineering Mathematics (for semester III) — Veerarajan T. — Tata McGraw-Hill
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