PAPER– I Total Marks: 100
Descriptive Statistics: (15%)
Nature and scope of Statistics. Organizing and classification of data.
Population and sample. Variables, Measurement scales.
Descriptive and Inferential Statistics. Description of data by frequency tables and graphs. Stem and leaf plot and Box and whisker plot.
Arithmetic Mean, Geometric Mean, Harmonic Mean, Mode, Median, Quartiles. Properties of Mean with proofs. Relative Merits and Demerits of various averages. Weighted Arithmetic Mean. Empirical Relation between Mean, Median and Mode. Absolute and Relative Measures of dispersion: Range, Semi-Inter Quartile Range, Mean Deviation, Variance, Standard Deviation, Coefficient of Variation, Coefficient of Mean Deviation, Coefficient of quartile Deviation. Properties of Variance and Standard Deviation with proofs. Standardized Variables. Moments, Moments Ratios, Sheppard‟s Correction, Skewness and Kurtosis. Chebechev‟s theorem and its
Concepts of Probability: (05%)
Operation in sets. Cartesian product set. Random experiment. Sample space and events. Rules of counting. Introduction to probability and axioms of probability, emphasising to concepts, facts, interpretation and illustrating examples. Basic laws of probability. Conditional and marginal probabilities. Independence of events. Baye’s theorem and its application.
Random Variable: (15%)
Discrete random variable. Probability function, probability distribution function. Mathematical expectation and its properties. Joint distribution of two discrete random variables. Marginal and conditional distributions. Mean, variance, moments, covariance and correlation of two discrete random variables. Moment generating function and its properties.
Continuous random variable. Probability distribution of a continuous random variable. Probability density function and probability distribution function. Joint distribution of two continuous random variables. Marginal and conditional distributions. Mathematical expectation and its properties. Moment generating function. Covariance and correlation of two random variables. Mean, Median, Mode, Geometric mean, Harmonic mean, Mean deviation, variance and moments of simple continuous functions.
Discrete Probability Distributions: (15%)
Uniform Bernoulli, Binomial, Multinomial, Hypergeometric, Poisson, Negative Binomial and Geometric distributions with their derivations, applications and fitting to statistical data. Poisson approximation to the binomial distribution.
Continuous Probability Distributions: (15%)
Uniform, Exponential and Normal distributions. Their properties, applications and fitting to statistical data. Normal approximation to the Binomial and Poisson distributions.
Bivariate Normal Distribution (10%):
Derivation, conditional density function, conditional expectation and moment generating function µ20, µ02 and µ11.
Method of Least Squares: (15%)
Scatter diagram, Principle of least square. Deduction and solution of normal equations of general linear model. Curve fitting. Equations of approximating curves by the method of least squares up to third degree polynomials. Fitting of exponential of the type (1) y=aebx (2) y = abx (3) y = axb.
Graphic representation of the curves. Interpolation and Extrapolation graphically. Criteria for fitting a suitable curve.
Regression and Correlation Analysis: (10%)
Logic of regression and correlation, scatter diagram. Regression models. Simple linear regression, least square estimates and their properties. Properties of Least Square regression line, standard error of estimate, co-efficient of determination. Multiple linear regression with two regressors, co-efficient of multiple determination. Partial and multiple correlation up to three variables. Linear correlation . Correlation co-efficient and its properties. Correlation of bivariate frequency distribution. Partial and multiple correlation for three variables. Rank correlation. Tied ranks.
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