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.
Text: Mathematical
Statistics with Application,
D.D.
Wackerly, W. Mandenhall & R.L. Scheaffer
7 th edition, Duxbury
|
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