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Generally topics like Distributions and density functions. Expectations; expectation of a function of a random variable.Uniform are considered very complex & an expert help is required in order to solve the assignments based on topics like normal and exponential random variables. Memoryless property of exponential distribution.Joint distributions & so on.

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- Recurrence and Transience , Convergence to Equilibrium , Applications, Measurability and sigma algebras. , Characteristic functions and generating functions. , Convergence of probability distributions, the , Central Limit Theorem. , Convergence of random variables. , The Law of Large Numbers. , Multivariate Normal distributions. , Conditional distributions. , Stochastic processes, Random walks, Branching processes, Poisson processes. , Wiener processes, concept of a random experiment, space of elementary events, sigma algebra of random events, Kolmogorov axiomatics, , Multivariate random variables, Marginal distributions, conditional distributions, Covariance matrix, Independence of random variables, correlation coefficient, regression, Laws of large numbers , central limit theorems, Axiomatic definition of probability
- Properties of probability measure, Conditional probability, stochastic independence, Random variables, distribution functions , density functions, Expectation , moments of random variables, Distributions of transformations of random variables, probability distributions, Multivariate random variables, Joint distributions, conditional distributions, Expectation, Covariance, correlation, Independence, expectation, Cauchy Schwartz inequality, Bivariate normal distribution, Density function, moments, marginal densities, conditional densities, Convergence of sequences of random variables, Laws of large numbers, Central limit theorems, statistical inference, Probability, distribution functions , distribution functions properties, classical discrete , continuous distribution functions, multivariate probability distributions , multivariate probability distributions properties, moment generating functions, simulation of random variables , R statistical package, Fundamental properties of probability, Probability measures, Random variables Independence, Sums of independent random variables, weak , strong laws of large numbers, Weak convergence, characteristic functions, central limit theorem, Elements of Brownian motion, probability theory, Measurability , sigma algebras
- Characteristic functions , generating functions, Convergence of probability distributions, Central Limit Theorem, Convergence of random variables, Law of Large Numbers, Multivariate Normal distributions, Conditional distributions, Stochastic processes, Random walks, Branching processes, Poisson processes, Wiener processes , Brownian motion, Probability Spaces and Sigma-Algebras,Extension Theorems: A Tool for Constructing Measures,Random Variables and Distributions,Integration,More Integration and Expectation,Laws of Large Numbers and Independence,Sums of Random Variables,Weak Laws and Moment-Generating and Characteristic Functions,Borel-Cantelli and the Strong Law of Large Numbers,Zero-One Laws and Maximal Inequalities,Independent Sums and Large Deviations,De Moivre-Laplace and Weak Convergence,Large Deviations,Weak Convergence and Characteristic Functions,Characteristic Functions and Central Limit Theorem,Central Limit Theorem Variants,Poisson Random Variables,Stable Random Variables, Higher Dimensional Limit Theorems,Infinite Divisibility and Levy Processes,Random Walks,Reflections and Martingales,More on Martingales,More on Martingales
- Even More on Martingales,Still More Martingales,Markov Chains,More Markov Chains,Additional Material on Markov Chains,Ergodic Theory,More Ergodic Theory,Ergodic Theory,Brownian Motion,More Brownian Motion,Even More Brownian Motion, random variation and probability including the probability axioms,Conditional probability and independence,Discrete probability models: the binomial, geometric and Poisson distributions. Discrete bivariate models,Continuous probability models: the uniform, exponential and Normal distributions,QQ-plot for Normal case,Bivariate continuous distributions, Words and Symbols of Higher Mathematics. Sample Spaces and Events,Axioms of Probability,Sampling,Sampling. Conditional Probability,Independence,More on Conditional Probability,Random Variables,Some discrete distributions,Continuous random variables, Probability axiomatics,Conditional probability,Independence,Random variables,Limit theorems for random variables,Sets,Conditional probability,Independence,Discrete random variables,Functions of random variables,Conditioning,Multiple random variables

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Topics like transformation of random variables (including Jacobians), examples. Simulation:generating continuous random variables & the assignment help on these topics is really helpful if you are struggling with the complex problems.

- PROBABILITY THEORY
- Events
- Notation
- Unions
- Intersections
- Complements of events
- Probabilities of events
- Probabilities of derived events
- Mutually exclusive events
- Independence of events
- Conditional probabilities of events
- An unfair die
- Probability
- Random variables and data
- The probability distribution of a discrete random variable
- Parameters
- Binomial distribution
- The mean of a discrete random variable
- The variance of a discrete random variable
- Many random variables
- Notation
- Independently and identically distributed random variables
- The mean and variance of a sum and of an average
- Two generalizations
- The proportion of successes in n binomial trials
- The standard deviation and the standard error
- Means and averages
- Continuous random variables
- Definition
- The mean and variance of a continuous random variable
- The normal distribution
- The standardization procedure
- Sums, averages and differences of independent normal random variables
- The Central Limit Theorem
- The normal distribution and the binomial distribution
- The chi-square distribution
- Conditional expectations
- Discrete time martingales
- Stopping times
- Uniform integrability
- Applications to 0-1 laws
- Radon-Nikodym Theorem
- Ruin problems, etc
- Local limit theorems
- Renewal theory
- Discrete time Markov chains
- Random walk theory
- n(v) ergodic theory
- Probability spaces as models for phenomena with statistical regularity.
- 7Discrete spaces (binomial, hypergeometric, Poisson)
- Continuous spaces (normal, exponential) and densities.
- Random variables
- Expectation
- Independence
- Conditional probability
- Introduction to the laws of large numbers and central limit theorem.