Introduction to Statistics

Population and Sample

Presentation of Data

Measures of Central Tendency

Measures of Dispersion

Moments

Skewness and Kurtosis

Negative Binomial Distribution

Moments Of Negative Binomial Distribution

Geometric Distribution, Moments Of Geometric Distribution And Mode Of Geometric Distribution

Hypergeometric distribution

Negative Hypergeometric Distribution

Uniform or Rectangular Distribution

Multinomial Distribution

Introduction To Probability

Definitions of Probability

Geometric Probability: Bertrand's Paradox,Fundamental Theorems on Probability,Addition Theorem of Probability (Theorem of Total Probability),Extension of Additive Theorem of Probability to n Events,B

Compound Events,Conditional Probability

Multiplication Theorem of Probability (Theorem of Compound Probability),Extension of Multiplication Theorem of Probability to n Events

Pairwise and Mutually Independent Events,

Baye's Theorem :Prior and Posterior Probabilities

Random Variables and Probability Distributions,Probability Mass Function,Discrete Probability Distribution

Distribution Function,Continuous Distribution,Probability Density Function

Cauchy Distribution

Characteristic Function Of Cauchy Distribution

Gamma Distribution

Moment Generating Function of Gamma Distribution, Harmonic Mean and Mode of Gamma Distribution

Beta Distribution

Mode of Beta Distribution of First kind and Beta Distribution of Second Kind

Negative Exponential Distribution

Interquartile Range, Mean Deviation about Mean and fitting of of Negative Exponential Distribution and Laplace Distribution

Moments and Moment Generating Function of Standard Laplace Distribution

Logistic Distribution and Properties of Negative Exponential Distribution

Weibull Distribution

Log-Normal Distribution

Modes of Convergence

Properties of Convergence and Convergence almost Surely

Properties of Convergence Almost Surely, Convergence In r^th Mean and convergence in Distribution

Inequalities

Chebyshev's Inequality

Generalized form of Bienayme-Chebysheve's Inequality, Applications of Chebyshev's inequality and Markov's inequality

problem of Chebyshev's Inequality and Weak Law of Large Number (WLLN)

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