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:
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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
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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)