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MATH 312:ORDINARY DIFFERENTIAL EQUATIONS I

STAT 111:Fundamentals of Probability and Statistics 2024

UNIVERSITY OF ELDORET

SCHOOL: SCIENCE               DEPARTMENT: MATHEMATICS AND COMPUTER SCIENCE

COURSE CODE: STAT 111                COURSE TITLE: FUNDAMENTALS OF PROBABAILITY AND STATISTICS.

CREDIT UNITS: 3                               PRE-REQUISITES: NONE

ACADEMIC YEAR: 2024/2025          SEMESTER: I, YEAR 2024

COURSE LECTURED BY: Koech       TEL: 0720775927

EMAIL: frkbuigut@gmail.com

GROUPS: AST, ACS, SC

Course Content

Descriptive statistics: definition of statistics, data and variables, sources and methods of data collection, representation of data; bar graphs, pie charts, frequency distribution (ogive). Measures of central tendency: Mean, median, mode, geometric and harmonic mean. Measures of dispersion: standard deviation, range, interquartile range, coefficient of variation, quartiles, deciles, percentiles. Skewness and kurtosis. Introduction to probability: experiments, sample space, event, probability of events, conditional probability, independence, addition and multiplication rules, Bayes’ theorem.

Purpose of the Course

The purpose of this course is to introduce learners to the concepts of statistics and probability, apply statistical concepts to real life problems.

Course Objectives

The objectives of this course are to:

i.               Introduce the students to basic statistics required for higher statistical courses.

ii.              Introduce students to the basic inferential statistics.

iii.            Demonstrate to students how to interpret statistics in different areas.

Expected Learning Outcomes

At the end of the course, the student should be able to:

i)               Represent data accurately using the right techniques.

ii)             Compute measures of central tendency, measures of dispersion, skewness and kurtosis.

iii)            Interpret and conclude measures of central tendency, measures of dispersion, skewness and kurtosis.

iv)            Solve problems involving basic probability.

v)             Describe and apply statistical concepts to real life situations.

WORK PLAN

WEEK

CONTENT COVERED

1

Introduction: Definitions- Data, statistics, types of statistics (Descriptive and inferential statistics), variables, sources and methods of data collection, population, sample, parameters, frequency distributions, arrays.

2

Representation of data: tallies, bar graphs/charts, pie charts, frequency distributions (ogives), histograms, pictograms.

3

Measures of central tendency: Ungrouped data- mean, mode, median, Geometric and harmonic means.

4

Measures of central tendency: Grouped data- mean, mode, median

5

Measures of dispersion: Ungrouped data- Range, mean deviation, variance, standard deviation, Grouped data- variance, standard deviation.

6

CAT 1

7

Measures of dispersion: Interquartile range, coefficient of variation, quartiles, deciles, percentiles, midrange, mid quartile, trimean.

8

Measures of shape: Moments of distributions, types of distributions and shapes, definition of skewness and kurtosis, computations of coefficients of skewness and kurtosis, interpretation of skewness and kurtosis values.

9

Introduction to probability: Definitions of probability, sets, subsets, experiments, sample space, events, probability of events, exclusive events.

10

Classical, subjective and relative frequency interpretation of probabilities, Venn diagrams.

11

CAT 2

12

Conditional probability, independence of events, general multiplication rules, conditional probabilities, Independent and dependent events, Special multiplication rule, General addition rule

13

Bayes’ rule/theorem, Tree diagrams

 

 

EVALUATION

CATs & ASSIGNMENTS

30%

EXAMINATION

70%

TOTAL

100%

 

REFERENCES:

1. Lipschutz, S. & Schiller, J.J. (2011). Schaum’s Outline of Introduction to Probability and Statistics (Schaums’s Outline Series). London: McGrawHill.

2. Rohatgi, V.K. & Saleh, A.K.E. (2001). An Introduction to Probability and Statistics. 2nd edition. Wiley Series in Probability and Statistics.

3. Ross, S.M. (2004). Introduction to Probability and Statistics for Engineers and Scientists. 3rd edition. Elsevier Academic Press.

4. Montgomery, D.C. & Runger, G.C. (2003). Applied Statistics and Probability for Engineers. 3rd edition. John Wiley & Sons, Inc.

5. Hogg, R. V., Mckean, J. and Craig A. T. (2012). Introduction to Mathematical Statistics (7th Edition).

6. Mann, P.N. (2001). Introductory Statistics. John Wiley & Sons Ltd.

7. Clarke, G.M. & Cooke, A. (2004). Basic Course in Statistics. 5th ed. Arnold.

8. Ross, S.A. (1994). First Course in Probability. 4th ed. Prentice Hall.

9. Crawshaw J. & Chambers J. (1994). A Concise Course in A-Level Statistics with Worked Examples. 3rd ed. Stanley Thornes.

10. Hogg, R.V. & Craig, A.T. (2004). Introduction to Mathematical Statistics. 5th edition, Higher Education Press.

11. Bain, L.J. & Engelhardt, M. (1992). Introduction to Probability and Mathematical Statistics. 2nd edition.

12. Hogg, R. V., Mckean, J. and Craig A. T. (2005). Introduction to Mathematical Statistics. 6th Edition. Pearson Education International.

 

 

 

 

 

 

 

 

 

MATH 112 :Discrete and Finite Mathematics 2024

APPLIED ENTOMOLOGY

Electricity, Magnetism, Optics and Modern Physics

1. Purpose of the Course This is the second part of the introductory physics course. The course reviews basic topics in electricity, magnetism, optics, and modern physics. 2. Course Objectives At the end of the course, the student should be able to: a) Define electric charge and describe its behaviour. b) Define and solve simple problems on electric forces and fields of discrete 12 charges. c) Carry out simple analysis of dc and ac circuits using Ohm’s law. d) Describe basic magnetic phenomenon. e) Explain how electromagnetism is produced and hence the operation of a transformer. f) Describe basic properties of light (reflection and refraction) and optical devices operating on these quantities. g) Describe wave nature of light – interference and diffraction. h) Describe the structure of an atom and binding energies; i) Describe radioactivity both quantitatively and qualitatively. 3. Course Content Electricity and magnetism: basic electrical concepts: electric charges, electric forces, electric field, current and voltage, ohms law, series and parallel resistive circuits. Properties of magnetic materials and their uses. Direct and alternating current, behaviour of R, L and C (resistance, inductance and capacitance). Measurement of R, L and C. Basic electronics: Diode and rectification; Transistors characteristics and application. Working principle and application of the cathode ray oscilloscope (CRO). Optics: Particle and wave theories. Review of mirrors and lenses. Defects in lenses. Different kinds of microscopes and telescopes. Phenomena of interference, diffraction and polarisation and their applications. Modern physics: Atomic structure: Bohr's theory and Heisenberg's quantum concept. Explanation of atomic spectra, X-rays. Structure of the nucleus. Natural and artificial radioactivity and its applications. Introduction to Nuclear fission, fusion and nuclear reactor