MA1L303
Undergraduate (ITEP)
· Generally offered: Spring
Probability and Statistics
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Basic Probability concepts, Random variables: Concept, cumulative distribution function, discrete and continuous random variables. Discrete random variables: Bernoulli’s trials, Binomial distribution, geometric distribution, Poisson distribution. Continuous random variables: Uniform distribution, exponential distribution, Gamma distribution, Normal distribution. Bivariate random variables: Joint distribution.
Unit II: Expected value of random variables: expectation, Raw and central moments of random variables, mean, variance, moment generating function, characteristics function, Median, Mode, covariance, correlation coefficient. Convergence in Probability: Tchebycheff’s inequality, properties of convergence, laws of large numbers, central limit theorem, approximation of distributions.
Unit III: Population, Finite and Infinite Population. Pseudo random variable, Theory of Sampling, parameter and statistic, estimator, Chi-square distribution, distribution of sample mean and variance, good estimator, Consistent & Unbiased estimates. Estimation of parameters: Maximum likelihood estimates, Confidence interval.
Unit IV: Testing of hypothesis: Problem, Different types of hypothesis, Formation of the problem – Probability of Type – I error, Probability of Type – II error, Best Critical region, Likelihood ratio testing, examples. Chi-square test of goodness of fit.
Full syllabus document →
Unit II: Expected value of random variables: expectation, Raw and central moments of random variables, mean, variance, moment generating function, characteristics function, Median, Mode, covariance, correlation coefficient. Convergence in Probability: Tchebycheff’s inequality, properties of convergence, laws of large numbers, central limit theorem, approximation of distributions.
Unit III: Population, Finite and Infinite Population. Pseudo random variable, Theory of Sampling, parameter and statistic, estimator, Chi-square distribution, distribution of sample mean and variance, good estimator, Consistent & Unbiased estimates. Estimation of parameters: Maximum likelihood estimates, Confidence interval.
Unit IV: Testing of hypothesis: Problem, Different types of hypothesis, Formation of the problem – Probability of Type – I error, Probability of Type – II error, Best Critical region, Likelihood ratio testing, examples. Chi-square test of goodness of fit.
2 questions tagged to this course
4
Votes
Is a matrix populated randomly by 0/1 invertible?
Suppose each entry of a $2\times 2$ matrix is populated with $0$ or $1$ independently with probability $1/2$. What is the probability that this matrix invertible? What will be the …