MA4110 Applied Statistics for Biotechnologists Syllabus:
MA4110 Applied Statistics for Biotechnologists Syllabus – Anna University PG Syllabus Regulation 2021
OBJECTIVES:
This course will help the students to
Study the mathematical aspects of probability, determination of probability and moments.
Study the distributions of discrete and continuous random variables and their properties.
Obtain the covariance and correlation between jointly distributed random variables, interpret simple linear regression and fitting of curves by least square method.
Study concepts and methods of sampling and various statistical tests in testing hypothesis on data.
Analyze one-way, two-way and three-way classifications of analysis of variance and problems using them.
UNIT I PROBABILITY AND RANDOM VARIABLES
Sample spaces – Events – Axiomatic approach to probability – Conditional probability – Additional theorem – Multiplication theorem – Baye’s theorem – Random variables : Continuous and discrete random variables – Distribution function – Expectation with properties – Moments, mean, variance problems – Continuous and discrete distributions.
UNIT II STANDARD DISTRIBUTIONS
Bivariate distribution – Conditional and marginal distribution – Discrete distributions – Binomial, Poisson, Geometric distributions – Continuous distributions – Normal, Exponential and Negative exponential, Gamma distributions – Simple problems – Properties.
UNIT III CORRELATION AND REGRESSION
Correlation coefficient – Properties – Problems – Rank correlation – Regression equations – Problems – Curve fitting by the method of least squares – Fitting curves of the form ax+b , ax2+bx+c, abx and axb -Bivariate correlation application to biological problems.
UNIT IV SAMPLING AND TESTING OF HYPOTHESIS
Concept of sampling – Methods of sampling – Sampling distributions and standard error – Small samples and large samples – Test of hypothesis – Type I & Type II Errors – Critical region – Large sample tests for proportion, mean – Exact test based on normal , t , F and Chi – square distribution problems – Test of goodness of fit.
UNIT V ANALYSIS OF VARIANCE
Basic principles of experimentation – Analysis of variance – One – way, Two – way classifications – Randomized block design – Latin square design – Problems.
TOTAL: 60 PERIODS
COURSE OUTCOMES
After completion of the course the students will be able to
CO1 Mathematical basis and foundations of probability and statistics, computation of probability and moments, standard distributions of discrete and continuous random variables and standard distributions and their properties
CO2 Compute the covariance and correlation between jointly distributed variables.
CO3 Compute and interpret simple linear regression and least square methods between two variables.
CO4 Methods of sampling and application of various statistical tests in testing hypotheses on data
CO5 One-way and two-way classifications of analysis of variance, properties and assumptions, randomized block design and Latin square design problems
REFERENCES:
1. Devore, J. L., “Probability and Statistics for Engineering & Sciences”, 8th Edition, Cengage Learning, 2014.
2. Gupta. S.C and Kapoor, V.K,. “Fundamentals of Mathematical Statistics”, 12th Edition, Sultan Chand and Sons, New Delhi, 2020.
3. Johnson, R.A., Miller, I and Freund J., “Miller and Freund’s Probability and Statistics for Engineers”, 9th Edition, Pearson Education, Asia, 2016.
4. Rice, J. A., “Mathematical Statistics and Data Analysis”, 3rd Edition, Cengage Learning, 2013.
5. Ross, S. M., “Introduction to Probability and Statistics for Engineers and Scientists”, 6th Edition, Elsevier, 2020.