American University Of Beirut | Faculty of Arts & Sciences | Statistics

Stat 230 - Introduction to Probability and Random Variables

Display of data, properties of probability, methods of enumeration, conditional probability and independent events; univariate and bivariate distributions corresponding to both discrete and continuous variables; mixture of distributions; covariance and correlation, independent random samples and the central limit theorem

Tutor: Team TOD

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Number of Lectures: 56
Approx. time to complete the course: 16 hrs.
Level: Undergraduate.
Students Enrolled: 7.
Access: 4 months.

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This course is given in parallel with the stat 230 course at AUB. Students who are taking the course and subscribe with us here, will need nothing beyond our services to ace the course.

Content

Lectures

chapter 1

Population, Sample, Dot Plot, Stem-and-Leaf Display 30 minutes
Frequencies, Relative Frequencies, Histograms 30 minutes
Population and Sample Mean 27 minutes
Median, Percentiles, Quartiles, Forth Spread, Boxplot 45 minutes
Population and Sample Standard Deviation, Variance 40 minutes
Skewness, Coefficient of Variation, Linear Transformation of Data 27 minutes

Chapter 2

Basic Set Theory, Sample Space, Events 23 minutes
Axioms and Properties of Probability, Equiprobable Sample Spaces 26 minutes
Counting Techniques, Permutation, Combination 60 minutes
Conditional Probability, Bayes' Formula, Independent Events 41 minutes
Chapter 2 Sample Exercises, Combination with Repetition 34 minutes
Chapter 2 Sample Exercises 44 minutes
Chapter 2 Sample Exercises Part 2 31 minutes

Chapter 3

Random Variables Types of Random Variables 33 minutes
Discrete Random Variables, Probability Mass Function and Cumulative Distribution Function 43 minutes
Expected Value of a Random Variable 23 minutes
Variance of a Random Variable, Standard Deviation, Linear Transformation 23 minutes
Binomial Random Variable, pmf, Mean, Variance 49 minutes
Hypergeometric, Negative Binomial RV, pmf, Mean, Variance 58 minutes
Poisson Random Variable, pmf, Mean, Variance, Approximating a Binomial RV 30 minutes
Sample Exercises Chapter 3 Part 1 42 minutes
Sample Exercises Chapter 3 Part 2 39 minutes

Chapter 4

Revision: Integration, Tabular Method 31 minutes
Continuous Random Variables, Probability Density Function and CDF 30 minutes
Percentiles, Median 28 minutes
Expected Values, Variance, The Uniform Distribution 27 minutes
Linear Tranformation of a Continuous RV, Motivating the Normal Distribution 29 minutes
Standard Normal Distribution, Normal Distribution, z-values, Percentiles, Critical Values 55 minutes
Approximating a Binomial RV with a Normal RV 28 minutes
The Exponential Distribution, The Markovian Property, Relation with Poisson RV 45 minutes
The Gamma Distribution, Incomplete Gamma Function, Chi-squared Distribution 32 minutes
The Poisson Process 32 minutes
Chebyshev's Inequality 34 minutes
Sample Exercises Chapter 4 Part 1 59 minutes
Sample Exercises Chapter 4 Part 2 42 minutes

Chapter 5

Joint pmf, Joint pdf, Marginal distributions: pdf and pmf, Independent Random Variables 48 minutes
Conditional probability density function, Sample Exercise 47 minutes
Expected Values, Variance, Covariance,Correlation 58 minutes
Bivariate Normal Disribution, Distributions of Maximum, Minimum ad Sum of Random Variables 43 minutes
Statistics, Simple Random Sample, Linear Combination of Random Variables (Expected value and Variance) 36 minutes
Sample Mean of a Normal Population, and a Large Population, Central Limit Theory (CLT) 60 minutes
Sample Exercises, Chapter 5 - 1 57 minutes
Sample Exercises, Chapter 5 - 2 68 minutes
Sample Exercises, Chapter 5 - 3 46 minutes
Sample Exercises, Chapter 5 - 4 49 minutes

Chapter 6

Point Estimates, Estimators, Standard Error, Unbiased Estimators, MVUE, Method of Moments 53 minutes

Chapter 7

Confidence Intervals, CI for a Population Mean (Known SD) 48 minutes
Large Sample CI for a population mean (Unknown SD) 34 minutes
CI for population proportion 43 minutes
CI based on Normal Population (Unknown SD) t distribution 32 minutes
CI for the Variance and SD of Normal Distribution, Chi-Squared distribution 22 minutes

Chapter 8

Testing a hypothesis, Null and alternative hypotheses, P-value, level of significance 42 minutes
Type I and II Errors 23 minutes
P-Values for Hypothese about a Population Mean (Normal Distribution), Finding a formula for the probability of Type II error 42 minutes
P-Values for Hypothese about a a Population Mean (t distribution. unknown SD), Population Proportion 50 minutes
Sample Exercises from Chapters 6,7,8 38 minutes

Course Notes

Course Notes

Stat 230 full notes

Course Exercises

Course Exercises

SampleExCh2
SampleExCh3
SampleExCh4_1
SampleExCh4_2
SampleExCh5
SampleEx6,7,8.pdf

Reviews

2 Reviews

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User

Omar B.

2 years ago

5 star rating

This is a VERY RICH course. Dense material, slow and clear explanation. Highly highly recommended !!

User

Marc K

2 years ago

5 star rating

I can't believe the patience put into this course. You should be teaching at AUB guys.

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