Basic Probability and Statistics | Department of Mathematics

Basic Probability and Statistics

Core course for B.Sc. (Research) Biotechnology. Only available as UWE with prior permission of Department of Mathematics. Does not count towards Minor in Mathematics.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures +1 tutorial weekly)

Prerequisites: Class XII Mathematics or MAT 020 (Elementary Calculus) or MAT 101 (Calculus I)

Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course provides an introduction to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course will act as an introduction to probability and statistics for students from natural sciences, social sciences and humanities.

Detailed Syllabus:

  1. Describing data: scales of measurement, frequency tables and graphs, grouped data, stem and leaf plots, histograms, frequency polygons and ogives, percentiles and box plots, graphs for two characteristics
  2. Summarizing data: Measures of the middle: mean, median, mode; Measures of spread: variance, standard deviation, coefficient of variation, percentiles, interquartile range; Chebyshev’s inequality, normal data sets, Measures for relationship between two characteristics; Relative risk and Odds ratio
  3. Elements of Probability: Sample space and events, basic definitions and rules of probability, conditional probability, Bayes’ theorem, independent events
  4. Sampling: Population and samples, reasons for sampling, methods of sampling, standard error, Population parameter and sample statistic
  5. Special random variables and their distributions: Bernoulli, Binomial, Poisson, Uniform, Normal, Exponential, Gamma, distributions arising from the Normal: Chi-­‐square, t, F
  6. Distributions of Sampling statistics: Sampling distribution of the mean, The central limit theorem, Determination of sample size, standard deviation versus standard error, the sample variance, sampling distributions from a normal population, sampling from a finite population
  7. Estimation: Maximum likelihood estimator; Interval estimates; Estimating the confidence interval for population mean, variance and proportions; Confidence intervals for the difference between independent means
  8. Hypothesis testing: Null and alternate hypothesis; Significance levels; Type  I  and  Type  II  errors;  Tests  based  on  Normal,  t,  F  and  Chi-­‐Square distributions for testing of mean, variance and proportions, Tests for independence  of  attributes,  Goodness  of  fit;  Non-­‐parametric  tests:  the sign test, the Signed Rank test, Wilcoxon Rank-­‐Sum Test.
  9. Analysis of variance: Comparing three or more means: One-­‐way analysis of variance, Two-­‐factor analysis of variance, Two-­‐way analysis of variance with interaction
  10. Correlation and Regression: Correlation, calculating correlation coefficient, coefficient of determination, Spearman’s rank correlation; Linear regression, Least square estimation of regression parameters, distribution of the estimators, assumptions and inferences in regression; analysis of residuals: assessing the model; transforming to linearity; weighted least squares; polynomial regression

Main References:

  • Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross, 2nd edition, Harcourt Academic Press.

Other References:

  • Basic and Clinical Biostatistics by Beth Dawson-­‐Saunders and Robert G. Trapp, 2nd edition, Appleton and Lange.
  • John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011.

Past Instructors: Sneh Lata, Suma Ghosh

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