Sr. No.

Content

Total 
Weightage 

Basic Probability:

Experiment, definition of probability, conditional probability, independent
events, Bayes’ rule, Bernoulli trials, Random variables, discrete random
variable, probability mass function, continuous random variable,
probability density function, cumulative distribution function, properties
of cumulative distribution function, Two dimensional random variables
and their distribution functions, Marginal probability function,
Independent random variables.

Some special Probability Distributions:

Binomial distribution, Poisson distribution, Poisson approximation to the
binomial distribution, Normal, Exponential and Gamma densities,
Evaluation of statistical parameters for these distributions.

Basic Statistics:

Measure of central tendency: Moments, Expectation, dispersion,
skewness, kurtosis, expected value of two dimensional random variable,
Linear Correlation, correlation coefficient, rank correlation coefficient,
Regression, Bounds on probability, Chebyshev‘s Inequality

Applied Statistics:

Formation of Hypothesis, Test of significance: Large sample test for single
proportion, Difference of proportions, Single mean, Difference of means,
and Difference of standard deviations.
Test of significance for Small samples:
t- Test for single mean, difference of means, t-test for correlation
coefficients, F- test for ratio of variances, Chi-square test for goodness of
fit and independence of attributes.