M.C.A 205: Probability and Statistics

Lectures: 4 Periods/Week Sessional Marks: 30
University Exam: 3 Hours University Examination Marks: 70


UNIT-I
Some probability laws
Axioms of Probability, Conditional Probability, Independence of the Multiplication Rule, Bayes' theorem
Discrete Distributions
RandomVariables , Discrete Probability Densities, Expectation and distribution parameters, Binomial distribution, Poisson distribution, simulating a Discrete distribution,
Continuous distributions
Continuous Densities, Expectation and distribution parameters, exponential distribution , Normal distribution,Weibull distribution and Reliability.

UNIT-II
Estimation: Point estimation, interval estimation and central limit theorem.
Inferences on the mean and the Variance of a distribution:
Hypothesis Testing, significance testing, Hypothesis and significance test on the mean, Hypothesis tests on the Variance
Inferences on proportions: Estimating proportions, testing hypothesis on a proportion,
Comparing two proportions: Estimation, comparing two proportions: hypothesis testing.

UNIT-III
Comparing two means and two variances: Point estimation: independent samples,
Comparing variances: The F-distribution,
Comparingmeans: Variances equal,
Analysis of Variance
One-way classification fixed effects model, comparing variances, pair wise comparisons, randomized complete block design

UNIT-IV
Simple linear regression and correlation
Model and parameter estimation, inferences about slope, inferences about intercept, Co-efficient of determination
Multiple linear regression models
Least square procedures for model fitting, a matrix approach to least squares, interval estimation.

Prescribed Book

  1. J Susan Milton and Jesse C. Arnold: "Introduction to Probability and Statistics", Fourth edition, TMH,(2007).
    Chapters:2, 3.1 to 3.3, 3.5,3.8,3.9,4.1,4.2,4.4,4.7.1,7.4, 8.3 to 8.6,9,10.1 to 10.3, 11.1, 11.3, 11.6, 12.1, 12.2, 12.4, 13.1 to 13.3,13.5.
Reference Books
  1. William Mendenhall, Robert J Beaver, Barbara M Beaver: Introduction to Probability and Statistics, Twelth edition, Thomson.