Courswork Problems (Probability and Stochastic Processes)

1) You have to solve all questions in attached file bellow. 2) You must explain clearly your calculations and what you have done. 3) you have to solve questions rely on these subjects: a) Discrete probability distributions, Bernoulli, Binomial, and Poisson. b) Continuous Probability Distributions. c) Integration. d) Continuous probability distributions, Uniform, Exponential, Normal. e) The normal approximation to the binomial and the lognormal [login to view URL] continuous probability distributions, their properties and expectations. f) Continuous probability distributions, Uniform, Exponential, [login to view URL] properties, expectations and variances. Discrete bivariate distributions,Their properties, expectations, and covariance. g) Distribution of the sums of random variables;Expectations and variance of the sums of random variables;The Central Limit Theorem h) The Central Limit Theorem;Confidence Intervals;Statistical Inference in the context of estimating the values of population parameters. i) Hypothesis Testing. j) Recursive Relations. k) Random Variable. l) Convergence of Random Variable. m) Law of large numbers and Central limit theorem. n) Estimation (Max. Likelihood Estimation and Method of Moment) o) Markov Chains and Processes.