# |
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 |
Lecturing, discussing, problem solving |
2 |
1.4 Combinations
1.5 Multinomial Coefficients
1.6 The Number of Integer Solutions of Equations |
Lecturing, discussing, problem solving |
3 |
II. Axioms of Probability
2.1 Introduction
2.2 Sample Space and Events
2.3 Axioms of Probability |
Lecturing, discussing, problem solving |
4 |
2.4 Some Simple Propositions
2.5 Sample Spaces Having Equally Likely Outcomes
2.6 Probability as a Continuous Set Function |
Lecturing, discussing, problem solving |
5 |
2.7 Probability as a Measure of Belief
III. Conditional Probability and Independence
3.1 Introduction
3.2 Conditional Probabilities |
Lecturing, discussing, problem solving |
6 |
3.3 Bayes’s Formula
3.4 Independent Events
3.5 P(·|F) Is a Probability |
Lecturing, discussing, problem solving |
7 |
IV. Random Variables
4.1 Random Variables
4.2 Discrete Random Variables
4.3 Expected Value |
Lecturing, discussing, problem solving |
8 |
4.4 Expectation of a Function of a Random Variable
4.5 Variance
4.6 The Bernoulli and Binomial Random Variables |
Lecturing, discussing, problem solving |
9 |
4.7 The Poisson Random Variable
4.8 Other Discrete Probability Distributions
4.9 Expected Value of Sums of Random Variables |
Lecturing, discussing, problem solving |
10 |
4.10 Properties of the Cumulative Distribution Function
V. Continuous Random Variables
5.1 Introduction
5.2 Expectation and Variance of Continuous Random Variables |
Lecturing, discussing, problem solving |
11 |
5.3 The Uniform Random Variable
5.4 Normal Random Variables
5.5 Exponential Random Variables |
Lecturing, discussing, problem solving |
12 |
5.5.1 Hazard Rate Functions
5.6 Other Continuous Distributions
5.7 The Distribution of a Function of a Random Variable |
Lecturing, discussing, problem solving |
13 |
VI. Jointly Distributed Random Variables
6.1 Joint Distribution Functions
6.2 Independent Random Variables
6.3 Sums of Independent Random Variables |
Lecturing, discussing, problem solving |
14 |
VIII Limit Theorems
8.1 Introduction
8.2 Chebyshev’s Inequality and the Weak Law of Large Numbers
8.3 The Central Limit Theorem
8.4 The Strong Law of Large Numbers |
Lecturing, discussing, problem solving |
15 |
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|
16 |
Final 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 |