# Statistics for SPPU 20 Course (SE - SEM IV -AI&DS)- 217528

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Unit I Introduction To Statistics And Sampling Theory Statistics : Introduction, Origin and Development of Statistics, Definition, Importance and Scope, Limitations, Distrust of Statistics Population and Sample : Sampling - Introduction, Types of Sampling, Purposive Sampling, Random Sampling, Simple Sampling, Stratified Sampling, Parameter and Statistic, Sampling Distribution, Statistical Inference, Sampling With and Without Replacement, Random Samples : Random Numbers, Population Parameters, Sample Statistics, Sampling Distributions. (Chapter - 1) Unit II Descriptive Statistics : Measures Of Central Tendency Frequency Distributions and Measures of central Tendency : Frequency Distribution, Continuous Frequency Distribution, Graphic Representation of a Frequency Distribution, Histogram, Frequency Polygon, Averages or Measures of Central Tendency or Measures of Location, Requisites for an Ideal Measure of Central Tendency, Arithmetic Mean, Properties of Arithmetic Mean, Merits and Demerits of Arithmetic Mean, Weighted Mean, Median, Merits and Demerits of Median, Mode, Merits and Demerits of Mode, Geometric Mean, Merits and Demerits of Geometric Mean, Harmonic Mean, Merits and Demerits of Harmonic Mean, Selection of an Average. (Chapter - 2) Unit III Descriptive Statistics : Measures of Dispersion Measures of Dispersion, Skewness and Kurtosis : Dispersion, Characteristics for an Ideal Measure of Dispersion, Measures of Dispersion, Range, Quartile Deviation, Mean Deviation, Standard Deviation and Root Mean Square Deviation, Coefficient of Dispersion, Coefficient of Variation, Skewness, Kurtosis. Correlation and Regression : Bivariate Distribution, Scatter diagrams, Correlation, Karl Pearson’s coefficient of correlation, Rank correlation, Regression, Lines of Regression, Regression Coefficients, Binomial and multinomial distributions, Poisson distribution, Uniform distribution, Exponential distribution, Gaussian distribution, Log-normal distribution, Chi-square distribution. (Chapter - 3) Unit IV Random Variables And Probabilty Distributions Random Variables and Distribution Functions : Random Variable, Distribution Function, Properties of Distribution Function, Discrete Random Variable, Probability Mass Function, Discrete Distribution Function, Continuous Random Variable, Probability Density Function. Theoretical Discrete Distributions : Bernoulli Distribution, Binomial Distribution, Mean Deviation about Mean of Binomial Distribution, Mode of Binomial Distribution, Additive Property of Binomial Distribution, Characteristic Function of Binomial Distribution, Cumulants of Binomial Distribution , Poisson Distribution, The Poisson Process, Geometric Distribution. (Chapter - 4) Unit V Inferential Statistics : Hypothesis Statistical Inference - Testing of Hypothesis, Non-parametric Methods and Sequential Analysis : Introduction, Statistical Hypothesis (Simple and-Composite), Test of a Statistical Hypothesis, Null Hypothesis, Alternative Hypothesis, Critical Region, Two Types of Errors, level of Significance, Power of the Test. (Chapter - 5) Unit VI Inferential Statistics : Tests For Hypothesis Steps in Solving Testing of Hypothesis Problem, Optimum Tests Under Different Situations, Most Powerful Test (MP Test), Uniformly Most Powerful Test, likelihood Ratio Test, Properties of Likelihood Ratio Test, Test for the Mean of a Normal Population, Test for the Equality of Means of Two Normal Populations, Test for the Equality of -Means of Several Normal Populations, Test for the Variance of a Normal Population, Test for Equality of Variances of two Normal Populations, Non-parametric Methods, Advantages and Disadvantages of Non-parametric Methods. (Chapter - 6)

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