Counting techniques, combinatorial methods, random experiments, sample spaces, events, probability axioms, some rules of probability, conditional probability, independence, Bayes' theorem, random variables (r.v.'s), probability distributions, discrete and continuous r.v.'s, probability density functions, multivariate distributions, marginal and conditional distributions, expected values, moments, Chebyshev's theorem, product moments, moments of linear combinations of r.v.'s, special discrete distributions, uniform, Bernouilli, binomial, negative binomial, geometric, hypergeoemtric and Poisson distributions, special probability densities, uniform, gamma, exponential and normal densities, normal approximation to binomial, distribution of functions of r.v.'s, distribution function and moment-generating function techniques, distribution of the mean, law of large numbers, the central limit theorem.

### Introduction to Probability (MATH 203)

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Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | * | ||

BA-Economics | * | ||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Electronics Engineering | * | ||

BS-Electronics Engineering | * | ||

BS-Industrial Engineering | * | ||

BS-Manufacturing Systems Eng. | * | ||

BS-Materials Sci. & Nano Eng. | * | ||

BS-Materials Science & Eng. | * | ||

BS-Mechatronics | * | ||

BS-Mechatronics | * | ||

BS-Microelectronics | |||

BS-Molecular Bio.Gen.&Bioeng | * | ||

BS-Telecommunications | * | ||

Mathematics |

### CONTENT

### OBJECTIVE

- To give an understanding of uncertainty and randomness

- To teach the fundemantal concepts and defintions of probability

- To equip the students with the tools and techniques of probability theory

### LEARNING OUTCOME

Upon completing this course students should be able to:

Use the basic principles of counting, permutations, combinations, and multinomial coefficients.

Perform set operations and compute elementary (conditional) probabilities.

Use the concept of random variables and their distributions, cumulative distribution functions.

Compute marginal distributions, conditional distributions and conditional expectations.

Evaluate mathematical expectations, moments, variances, co-variances, conditional expectations, and moment-generating functions.

Investigate the basic properties of important discrete and continuous random variables such as Bernouilli, binomial, hypergeometric, Poisson, uniform, exponential, gamma and normal.

Implement different techniques such as the distribution function technique, the moment generating function technique, the transformation technique to evaluate the distribution of functions of random variables.

Investigate the properties of various statistics (sample mean, sample variance, order statistics) taken from a population.

See the applications in various disciplines.

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 35 |

Midterm | 35 |

Assignment | 20 |

Participation | 10 |

### RECOMENDED or REQUIRED READINGS

Textbook |
John Freund's Mathematical Statistics with Applications, 8th Edition, Pearson- |

Optional Readings |
Supplementary Texts : |