# |
Learning Outcomes |
1 |
Students will be able to define the relevant random events of a random experiment and to compute the probabilities of simple and composition of events |
2 |
Students will be able to check the independence of events, to compute the conditional probabilities, and to use Bayes’ Theorem. |
3 |
Students will be able to compute probabilities related to a random variable, expected value and variance of a random variable using probability mass function, probability density function, cumulative distribution function. |
4 |
Students will know and use properties of some well-known discrete and continuous probability distributions. |
5 |
Students will be able to use joint distributions to compute probabilities of events in more than one random variable, to compute marginal distributions, and to compute the distributions of functions of two random variables. |
6 |
Students will know properties of random samples and the distributions of the sample mean and sample variance. |
# |
Subjects |
Teaching Methods and Technics |
1 |
I. Combinatorial Analysis
1.1 Introduction
1.2 The Basic Principle of Counting
1.3 Permutations |
Lecture, discussion, presentation |
2 |
1.4 Combinations
1.5 Multinomial Coefficients
1.6 The Number of Integer Solutions of Equations |
Lecture, discussion, presentation |
3 |
II. Axioms of Probability
2.1 Introduction
2.2 Sample Space and Events
2.3 Axioms of Probability |
Lecture, discussion, presentation |
4 |
2.4 Some Simple Propositions
2.5 Sample Spaces Having Equally Likely Outcomes
|
Lecture, discussion, presentation |
5 |
2.6 Probability as a Continuous Set Function
2.7 Probability as a Measure of Belief |
Lecture, discussion, presentation |
6 |
III. Conditional Probability and Independence
3.1 Introduction
3.2 Conditional Probabilities
3.3 Bayes’s Formula |
Lecture, discussion, presentation |
7 |
3.4 Independent Events
3.5 P(·|F) Is a Probability |
Lecture, discussion, presentation |
8 |
Midterm Exam |
Exam |
9 |
IV. Random Variables
4.1 Random Variables
4.2 Discrete Random Variables
4.3 Expected Value |
Lecture, discussion, presentation |
10 |
4.4 Expectation of a Function of a Random Variable
4.5 Variance
4.6 The Bernoulli and Binomial Random Variables |
Lecture, discussion, presentation |
11 |
4.7 The Poisson Random Variable
4.8 Other Discrete Probability Distributions
4.9 Expected Value of Sums of Random Variables
4.10 Properties of the Cumulative Distribution Function |
Lecture, discussion, presentation |
12 |
V. Continuous Random Variables
5.1 Introduction
5.2 Expectation and Variance of Continuous Random Variables
5.3 The Uniform Random Variable
5.4 Normal Random Variables |
Lecture, discussion, presentation |
13 |
5.5 Exponential Random Variables
5.5.1 Hazard Rate Functions
5.6 Other Continuous Distributions
5.7 The Distribution of a Function of a Random Variable |
Lecture, discussion, presentation |
14 |
VI. Jointly Distributed Random Variables
6.1 JointDistributionFunctions
6.2 Independent Random Variables
6.3 Sums of Independent Random Variables
6.4 Conditional Distributions: Discrete Case |
Lecture, discussion, presentation |
15 |
6.5 Conditional Distributions: Continuous Case
6.6 Order Statistics
6.7 Joint Probability Distribution of Functions of Random Variables
6.8 Exchangeable Random Variables |
Lecture, discussion, presentation |
16 |
Final Exam |
Exam |
# |
Learning Outcomes |
Program Outcomes |
Method of Assessment |
1 |
Students will be able to define the relevant random events of a random experiment and to compute the probabilities of simple and composition of events |
1͵7 |
1͵2 |
2 |
Students will be able to check the independence of events, to compute the conditional probabilities, and to use Bayes’ Theorem. |
1͵7 |
1͵2 |
3 |
Students will be able to compute probabilities related to a random variable, expected value and variance of a random variable using probability mass function, probability density function, cumulative distribution function. |
1͵7 |
1͵2 |
4 |
Students will know and use properties of some well-known discrete and continuous probability distributions. |
1͵7 |
1͵2 |
5 |
Students will be able to use joint distributions to compute probabilities of events in more than one random variable, to compute marginal distributions, and to compute the distributions of functions of two random variables. |
1͵7 |
1͵2 |
6 |
Students will know properties of random samples and the distributions of the sample mean and sample variance. |
1͵7 |
1͵2 |