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SM-2205 Intermediate Statistics Module Code : SM-2205 Intermediate Statistics Core 4 Student Workload : 8-10 hours/week Contact hours for timetabling : 4 hours/week SM-1202 Prerequisite : SM-2403 Anti-requisite : Aims: This is an intermediate level course in Probability and Statistics that aims to broaden the probabilistic and statistical concepts and techniques of A-level mathematics so as to provide a more extensive knowledge base in the theoretical and applied aspects of these areas. On completing this module, the student should be able to organise and describe of data, produce histograms and stem plots, solve problems involving probability, conditional probability and the Bayes rule, find probabilities and moments related to univariate and multivariate distributions, approximate binomial distribution using Poisson and normal distributions, compute conditional probabilities, conditional expectation, covariance and correlation for jointly distributed random variables, find sampling distributions of statistics, solve large sample probability problems using the central limit theorem, compute confidence intervals and perform hypothesis testing, compute the correlation and estimate the regression coefficients for bivariate data, compute confidence intervals and perform hypothesis testing for regression coefficients, find prediction and confidence intervals for predicted values, and solve problems related to the bivariate normal distribution. The student will also learn to use a statistical software package. Module Title : Type of Module : Modular Credits : Module Content: Descriptive statistics: organization and description of data, frequency distributions; measures of location – mean, median, mode, quartiles; measures of dispersion – variance, standard deviation, range, interquartlie range. Probability: non-deterministic experiments, sample space, events, probability – definition and properties, conditional probability, independence, Bayes’ theorem. Discrete probability distributions: discrete random variables; probability mass function and cumulative distribution function of discrete random variables; expectation, variance and standard deviation of discrete random variables; special discrete distributions – Bernoulli, discrete uniform, binomial, hypergeometric, Poisson, geometric and negative binomial. Continuous probability distributions: continuous random variables, probability density function and cumulative distribution function of continuous random variables; expectation, variance and standard deviation of continuous random variables; special continuous distributions - uniform, exponential, gamma, beta, Weibull and normal. Approximation results: Chebyshev's inequality; Normal and Poisson approximations to binomial. Statistical inference: sampling distributions; the central limit theorem; estimation and confidence intervals; statistical hypothesis testing, critical region, significance level and power and p-values; confidence intervals for the population mean, the population variance and the population proportion; z-test and t-test for the population mean;z-test for the population proportion and chi-square test for the population variance; confidence intervals for difference of means, difference of proportions and ratio of variances; two-sample z-test and t-tests for testing equality of means and equality of proportions; F-test for testing equality of variances. Joint distributions: joint, marginal and conditional distributions for discrete and continuous random variables; conditional expectation, covariance and correlation for jointly distributed random variables; bivariate normal distribution and related concepts. Regression: linear regression and estimation of the regression function; least-square method; computation and properties of parameter estimators; confidence intervals and tests of hypothesis for the slope and intercept parameters. prediction and confidence intervals for the predicted value of the dependent variable for a given value of the independent variable Use of a statistical software package such as Minitab. Assessment: Examination: 60% Course Work: 40% (2 class tests, 20% each)