MCA -Master of Computer Applications Second Semester Stats and Numerical MathsUniversity Syllabus and Classes of MCA Second Semester Stats and Numerical Maths
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MCA FIRST YEAR ( SEMESTER -2 )
2CSA-5 Statistics & NUMERICAL MATHEMATICS
Unit – 1 introduction – definition of statistics, importance and scope of statistics, Limitations of statistics, Distrust of statistics.
Statistical data collection – primary and secondary data, Methods of collecting primary data, sources and secondary data census and sample investigation.
Presentation of statistical data – classification, tabulation, frequency distribution, diagrams and graphs.
Frequency distributions and Measure of Central Tendency – Frequency distribution, continuous Frequency distribution, Graphic Representation of a Frequency Distribution average or measures of central tendency or measures of Locations, Requisites for an ideal measure of central tendency – Arithmetic: Mean, Median, mode, geometric Mean and harmonic mean, eighted average, relationship amongst different averages.
UNIT – 2 Measures of dispersion, skewness and kurtosis – Meaning and significance of dispersion, Methods of measuring Dispersion – Range, quartile, mean deviation, standard deviation, coefficient of skewness, kurtosis, coefficient of dispersion, coefficient of variation.
Correlation and regression – definition of correlation, scatter diagram, karl pearson Coefficient of correlation, limits for correlation coefficient, definition of Regression, lines of Regression, Regression Curves, Regression Coefficients, properties of Regression coefficients, correlation analysis vs. Regression analysis.
UNIT – 3 Probability – Introduction, Definitions of various Terms, Mathematical or classical Probability, statistical or Empirical Probability Statistical or Empirical Probability, Mathematical Tools, sets and Elements of sets, operations on sets, axiomatic Approach to Probability, Probability function, Mathematical law of Addition of Probabilities and Conditional Probabilities, Independent event, bayes Theorem Geometric probability.
UNIT - 4 Random variables and Distribution functions – definition of random variable, distribution function, properties of Distribution function, Discrete Random variable, Probability density function, continuous random variable, continuous density function, continuous distribution function.
Mathematical Expectation and Generation function – Definition of mathematical expectation, addition & multiplication Theorem of expectation, co-variance, Expectation & variance of a Linear combination of random variables, moment generation function, some limits of moment Generating function, theorem of moment generating function, cumulants.
UNIT – 5 Theoretical discrete distributions – Introduction, Bernoulli distribution, Binomial Distribution, Poisson Distribution, Geometric Distribution.
Theoretical Continuous Distributions – Introductions normal distribution, game distribution, cauchy’s Distribution and central limit theorem.
BCA Bachelor Of Computer Application, BCCA, Bachelor of Commerce & Computer Application BE IT/CS, Information technology/Computer Science MCA, Master of Computer Application MCM, Master of Computer Management Diploma , Polytechnic Others,