Course Code: MCA412
Course Title: Probability and Statistics (4 Credits)
Unit-1: Probability: Random experiment, outcome, trial and event, Exhaustive events, favourable events, Independent events, sample space, definition of probability, addition theorem of probability, conditional probability, independent events, Mutually and pair wise independent events, multiplication theorem of probability for independent events, Baye’s theorem.
Unit-2: Random Variable (Univariate): Random Variable, Distribution function, discrete random variable, Probability mass function, Distribution function of discrete random variable, Continuous random variable, Probability density function. Distribution function of continuous random variable. Two dimensional probability mass function, Marginal probability function, conditional probability function, Two dimensional distribution function, marginal distribution function, Joint density function, marginal density function.
Unit-3: Mathematical Expectations: Definition, Expected value of random variable, expected value of function of a random variable, properties of expectations, Various measures of Central Tendency, Dispersion, skewness and Kurtosis for continuous probability distribution, continuous distribution function, Variance, Properties of variance, covariance.
Unit-4: Moment Generating Function: Definition, Properties of moment generating function, cumulants.
Unit-5: Measures of Central Tendency: Explain the meaning and application of averages, define the meaning and calculation of positional averages, and discuss merits, demerits and limitations of averages.
Unit-6: Measures of Dispersion: Explain the meaning of dispersion, describe the measures of dispersion, and classify the measures of shape of data.
Unit-7: Moments: Raw and central moments. Relation between moments : raw moments & central moments, Effect of change of origin and scale on moments, Pearsonian coefficients Measures of skewness, kurtosis.
Unit.-8: Standard Distribution: Binomial, Poisson, Negative Binomial Distribution, Normal Distribution and their properties.
Unit-9: Correlation & Regression: Explain the meaning of correlation and regression, measure the coefficients of correlation and regression, and define and measure coefficient of determination.
Unit-10: Index Numbers: Learn about the need of index numbers, explain the different methods of constructing index numbers, evaluate the tests for judging the soundness of an index number.
Unit-11: Time Series: Explain about time series, describe components of time series, and define measurement of variations of time series.
Unit-12: Sampling Theory: Sampling Theory, Random Samples and random Numbers, Sampling with and without replacement, sampling distributions, sampling distribution of means, sampling distribution of properties, sampling distribution of differences and sum, standard errors, software demonstration of elementary sampling Theory.
Unit-13: Hypothesis Testing: Explain meaning of hypothesis, interpret statistical procedure of hypothesis testing, use application of hypothesis testing in several business contexts.
Unit-14: Tests Of Significance: Based On t, F and Z Distributions:-Student’s (t) distribution, definition, properties, critical value of t, Application of t-distribution, Test for single mean, t-test for difference of mean, Fischer Z- transformation, F-statistic, critical value of F distribution, application.