BT2022 | COURSE MATERIALS | JAN-MAY 2023
NOTE: send all the queries to rmurugan.working@gmail.com
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01 Random variable, concept of probability and probability density function, population, sample, estimates and parameters
02 Expectation operator formalism, independent and identically distributed random variables
04 Characteristic function and moments of probability density function
05 moment and cumulant generating function
07 Differential and statistical equation of normal density function
08 Standard normal deviate; Elementary convergence theorems
09 Law of large numbers (LLN)
10 Central limit theorem (CLT)
11 Student’s theory on the probable error of the sample means derived from normal populations
12 Distribution of sample means and variances derived from normal populations
13 Student theorem, Chi-square and t-distributions
14 Probable range of population mean and variance
15 Fisher F distribution on the ratio of sample variances derived from normal population
16 Statistical comparison of two different sample means or sample variances
17 Formulation of null and alternate hypothesis
18 Test of significance and confidence level
19 Type I and II errors
20 t-test, F-test and Chi-square tests
21 Multiple comparison problem
22 Concept of family wise error rate (FWER) and false discovery rate (FDR)
23 Control of FDR, Bonferroni and Benjamini procedures
24 Multidimensional statistics; bootstrap methods.
25 Correlation and regression
26 Linear and nonlinear regression of two variables
27 Multiple linear regression analysis
28 Pearson linear least square fitting procedure
29 nonlinear least square fitting using Marquardt-Levenberg algorithm
30 Design of experiments in biology
31 completely randomized design (CRD)
32 Randomized block design (RBD)
33 Development and Application of statistical workflows
34 Microarray data analysis
35 Stochastic processes, Langevin equation
36 Brownian motion
37 Fluctuation dissipation theorem
38 stochastic chemical kinetics
39 Master equations
40 Gillespie algorithm
41 Stochastic gene expression.