BCA Semester II - Fundamentals of Probability and Statistics

UNIT-I 

Introduction: Importance of Statistics, Concepts of Statistics, population and a sample; quantitative and qualitative 

data; Collection of Primary and Secondary data; Classification and Tabulation of data. Construction of Univariate and 

bivariate frequency distribution; Diagrammatic and Graphical representation of data.

UNIT-II 

Descriptive Statistics: Measures of central tendency: Arithmetic Mean, Median, Mode, Geometric mean, Harmonic 

mean; Measures of Dispersion:Range, Quartile deviation, Mean deviation, Standard deviation.

Definition of Moments; Measures of Skewness: Karl pearson’s coefficient of skewness, Bowley’s coefficient of 

skewness; Kurtosis.

UNIT-III 

Probability:Basic terminology, Mathematical probability, Statistical probability, Axiomatic approach to probability, 

Theorems onprobability.

Conditional Probability, Multiplication theorem of probability, Independent events, Pairwise/mutually independent 

events, Bayes’ Theorem.

UNIT-IV 

Random variable: Definition of a random variable, discrete and continuous random variables, functions of random 

variables, probability mass function and probability density function and mathematical expectation of a random variable 

and properties of expectation.

Probability Distributions:Binomial, Poisson and Normal Distribution.

UNIT-V 

Correlation and Regression analysis:Definitionof correlation, Scatter Diagram, Karl Pearson’s Coefficient of 

correlation; Partial and Multiple correlation coefficients (for three variables); Definition of Regression, Simple Linear 

Regression (for 2 variables).

Small Sample Tests:Basic Definitions of testing of hypothesis;t-Test: t-test for single Mean, t-test for difference of 

Means, Paired t-test. F-Test: F-test for equality of two population variances. CHI-SQUARE Test:test for single 

variance(population variance)and test of independence of attributes.