University of Northern British Columbia

MATH 371-3: Probability & Statistics for Scientists and Engineers

Course Objective:       To prepare a solid foundation of probability and statistical theory and learn its importance in solving real-world problems involving uncertainties.

 

                                    This course is a calculus-based introduction to the theory and application of probability and statistics. The topics to be covered include concepts of probability, events  and populations, probability theorems, concept of a random variable, continuous and discrete random variables, probability                                                  distributions, distributions of functions of  random variables, moments, Tchebyshev's inequality,   central limit theorem, sampling and statistical                                                           estimation theory, hypothesis testing, simple regression analysis and design of experiments.

 

 

Instructor:                    Dr. Pranesh Kumar, Office: LIB 10-2510, Tel: 250-960-6671.

                                    Kumarp@unbc.ca

 

Text:                            Mathematical Statistics with Application,

                                    D.D. Wackerly, W. Mandenhall & R.L. Scheaffer

                                    7 th edition, Duxbury

 

 

Topics:

 

Chapter/Sections/Topics

Suggested practice exercises  (6th ed)

 

Suggested practice exercises  (7th ed)

 

1 Introduction : Statistics and Probability

 

2. Probability:  (Sec 2.1, 2.3 - 2.11)

Introduction, Events, Probabilistic model, Calculating probability, Counting rules, Laws of probability, Bayes’ rule

 

 

 

 

Ch 2:  2,5,9,17,23,27,33,43,54,57,61, 65,71,81,85, 87,93,99,107,111,113,121, 131,137

 

 

 

Ch 2:  2 7 11 19 31 35 41 53 68 71 77 81 95 105 109 111 117 125 131 133 143 155 163

3. Discrete random variables & probability distributions: (Except Sec 3.10)

Probability distribution, expected values, binomial,geometric,negative binomial, hypergeometric, Poisson distributions, moments, Tchebysheff’s theorem.

 

Ch 3: 1,3,9,13,19,23,31, 37,45,55,65,79, 85,101,107,111,117,123,131,133,150,155,159,165

Ch 3: 1 3 9 19 25 33 43 49 61 71 83 97 103 127 135 139 147 155 167 169 188 193 197 205 

4. Continuous random variables &  

 Probability distributions: (Sec 4.1 - 4.7, 4.9)

Probability distribution,expected values, uniform, normal,(gamma, exponential, beta distributions)*

 

Ch 4: 1,7,11,23,31,39,57,71,77,78,89, 97,101, 133,139,149

Ch 4: 5 13 17 29 41 51 71 92 97 98 111 129 133 165 171 183

5. Multivariate probability distributions:

 (Sec 5.1 - 5.8)

Bivariate distributions, marginal/ conditional distributions, expected values of  functions of variables, covariance

 

Ch 5: 3,13,19,29,45,51,65,69,77,81,88, 91,93

Ch 5:3 15 21 33 53 59 77 81 91 95 104 107 109

6. Functions of random variables: (Sec 6.1- 6.4)

Methods of distribution functions and transformations  

 

Ch 6: 1,3,5,20,23,27

Ch 6: 1 3 5 24 27 31

 7. Sampling distributions and Central limit theorem (7.1-7.3)

 

Ch 7: 5,7,8,11,19,25,28,37,47,50,59,61

Ch 7: 1 3 15 16 21 37 45 48 57 73 76 85 87

8-9. Estimation and Methods of estimation (8.1-8.8) , (9.1-9.4, 9.7)

Point estimators & properties, confidence intervals, sample size selection, maximum likelihood estimation *

 

Ch 8: 1 5 9 13 17 19 21 23 25-27 29 31 35 37 45 51 55 57 63 65 69 71 73 

 

Ch 9: 2 3 6 13 19 25 29 31 35 37 39 48-50 77 78 80

Ch 8: 1 91 13 17 21 23 25 27 33 35 39 41 59 62 67 69 83 85

 

Ch 9: 2 3 6 19 15 31 37 39 43 45 47 56-58 85 86 88

10. Hypothesis testing (10.1-10.3,10.5-10.6,10.8)

Elements of statistical test, large & small sample tests, p-values

 

Ch 10: 3 11 15 23 37 41 47 57 61 65 

 

Ch 10: 3 21 26 33 47 51 57 69 73 77

 

11. Linear model and Estimation by least squares  (11.1-11.5, 11.7-11.8)

Linear model, least squares method, inference concerning parameters *, prediction, correlation

 

Ch 11: 6 11 26(a) 42 71-72

Ch 11: 10 15 30(a) 46 51

12. Designing experiments (12.1-12.4)

Designing experiments, elementary designs

Ch 12: 1-4  13  16-17 25

 

Ch 12: 1-4  15  18-19 27

 

 

 

 

Lectures

 

Introduction

Chapter1

Chapter2

Chapter3

Chapter4

Chapter5

Chapter6

Chapter 7