M.C.A. Semester II: Probability and Statistics

SYLLABUS OF PROBABILITY AND STATISTICS  Unit I      Sample Space, Events, Axioms of Probability, Probability Space, Probability of Composite Events, Conditional Probability, Bayes Theorem, Independent Events  Unit II      Single Random Variable, Distribution and Density Functions, Expectation values, Moments, Definition of Median, Mode. Measure of dispersion, Skewness and Kurtosis. Characteristic and Moment generating functions. Examples of Discrete Random variables (Bernoulli trials, Poisson variables, geometric   distribution) and Continuous random variable (Normal distribution, Beta and Gamma distributions)  Unit III   Two Random variables. Joint probability distribution and density functions. Marginal and Conditional distributions. Correlation coefficient and ratio. Independent variables. Many random variables. Correlation matrix.  Unit IV      Statistics. Frequency distribution. Geometric and Harmonic mean. Parameter Estimation, Biased and Unbiased Estimators, Efficient Estimator, Optimal Estimator, Sufficient Estimator. Hypothesis testing. Chi Square test. Student t-test.  Unit V      Single server queue. Erlang distribution and Poisson Process. Stationary queue. Non-Erlang arrivals and modification of steady state queue concepts. Term work/Practicals : Each candidate will submit a journal in which assignments based on the above syllabus and the internal test paper. Test graded for 10 marks and Practicals graded for 15 marks. References :  Introduction to Probability &amp; Statistics, Menclenhall 12th edition, Thomson </li>  Introduction to Probability &amp; Statistics J.Susan Milton, Jesse C. Arnold Tata McGraw Hill </li>  Probability and its computer applications : Kishore Trivedi, PHI </li>  Schaum’s Outlines Probability, Random Variables &amp; Random Process Tata McGraw Hill </li>  Fundamental of Mathematical Statistics – S.C.Gupta, V.K.Kapoor </li> </ol>

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