Instructor
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Course Recorded by: Dr. Saleha Naghmi Habibullah
PhD
National College of Business Administration & Economics (NCBAE)
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Probability - Some Basic Terms
Random Variable - Concept
Random Variable - Example
Random Variable - Discrete Data
Probability Mass Function (PMF) - Concept
Probability Mass Function (PMF) - Example
Random Variable - Continuous Data
Probability Density Function (PDF)
Probability Generating function (PGF)
Mean and Variance of PGF
Some well-known PGF
Linear Combination of PDFs
Cumulative Distribution Function (CDF) - Concept
Cumulative Distribution Function (CDF) - Example Discrete Case
Obtaining PMF from CDF
Cumulative Distribution Function (CDF) - Example Continoius Case
Two Random Variables Being Equal in Distribution
Cumulative Distribution Function (CDF) - First Property
Cumulative Distribution Function (CDF) - Second Property
Cumulative Distribution Function (CDF) - Third Property
Cumulative Distribution Function (CDF) - Fourth Property
Evaluating Probabilities using CDF
Derivation of CDF is PDF
In Continuous case, Probability does not exist at ANY particular point
Monotonicity - Concept
Total Probability is one
Finding an Unknown constant from PMF
Finding an Unknown constant from PDF
Transformation of Discrete variables - one to one case
Transformation of Discrete variables - NOT one to one case
Transformation of Continuous variables
Transformation of Continuous variables - Jacobian Transformation
Transformation of Continuous variables - Jacobian Transformation - Example 1
Transformation of Continuous variables - Jacobian Transformation - Example 2
Mode of Discrete variable
Mode of Continuous variable
Median of Discrete variable
Median of Continuous variable
Percentile of Continuous variable - Concept
Percentile of Continuous variable - Example
Inverse CDF (Quantile Function)
One random variable is larger than other random variable
Mathematical Expectation of variable - Concept
Mathematical Expectation of a function - Concept
Mathematical Expectation - Linear Combination of Expected Values
Mathematical Expectation of a function - Discrete case example 1
Mathematical Expectation of a function - Discrete case example 2
Mean, Variance and Standard Deviation of random variable - A theorem
Mean, Variance and Standard Deviation of random variable - Discrete case
Degenerate random variable - Concept
Mean of the symmetric distribution - Proof
Mean and variance of standardized variable - Proof
Moments - concept
Moments Ratios
Moment Generating Function (MGF) - Concept
Moment Generating Function (MGF) of some well-known distributions
General Rule for the product of Expected Value
Mathematical Expectation - Another way of computing
Derivation of Mean and Variance from MGF
Derivation of m-th Moment from MGF
Derivation of m-th Moment about an Arbitrary origin from MGF
Alternative Method of finding moments from MGF Using Maclaurins's Series
Relationship between MGF of Standardized variable and MGF of original variable - Theorem 1
Relationship between MGF of Standardized variable and MGF of original variable - Theorem 2
Cumulant Generating Function (CGF)
Cumulant Generating Function (CGF) - Additive Property
Relationship between Central MGF and CGF
Chevbyshev's Inequality - Concept
Chevbyshev's Inequality - Example
Chevbyshev's Inequality - Another form of presenting it
Relationship between Harmonic Mean, Geometric Mean and Arithmetic Mean
Random Vector - Concept
Event in case of a two-dimensional space - Concept
Joint Cumulative Distribution Function
Discrete Random Vector and Joint Probability Mass Function
Support of Discrete Random Vector - Concept
Continuous Random Vector and Joint Probability Density Function
Determination of the probability of an event - Continuous Vector
Support of Continuous Random Vector - Concept
Properties of joint cumulative probability distribution function (Part 1)
Properties of joint cumulative probability distribution function (Part 2)
Marginal Probability Mass Function - Concept
Marginal Probability Mass Function - Example
Marginal Probability Density Function - Concept
Computations of Probabilities that cannot be found through Marginal PDFs
Expected Value of a function of a Random Vector
Computations of Probabilities for Continuous Random Vector
Expectation of the product of the two random vectors - Discrete case
Expectation of the product of the two random vectors - Continuous case
Expectation of the Ratio of two random vectors - Continuous case
Moments from MGF of Random Vector
Expected value of Random Vector
Linear Combination of Expected Values of Function of a Random Vector
Transformation of a Bivariate Probability Mass Function - Example 1
Transformation of a Bivariate Probability Mass Function - Example 2
Transformation of a Bivariate Probability Density Function - Using Jacobean
Transformation of a Bivariate Probability Mass Function - Using MGF
Characteristic Function
Derivation of Mean and Variance of a distribution using Characteristic Function
Conditional Distribution - Concept
Conditional Expectation Conditional Mean and Variance
Conditional Expectation - Theorem
Correlation Coefficient of Bivariate Distribution
Correlation Coefficient - Properties (1st)
Correlation Coefficient - Properties (2nd, 3rd)
Correlation Coefficient - Properties (4th, 5th, 6th)
Correlation Coefficient - Computation in case of joint PDF
Conditional Distribution - Variance of joint PDF of two random variables - Example
Conditional mean of Y given X that is LINEAR in X
Independent Random Variables - Concept
Independent Random Variables - Example
Independent Random Variables - Theorem X and Y are independent if and only if F(x,y) = FX(x)FY(y)
Independent Random Variables - Theorem X and Y are independent then E[u(X1)v(X2)] = E[u(X1)] E[v(X2)]
Independent Random Variables - Theorem X and Y are independent if and only if the joint MGF show M(t1,t2)= M(t1,0) M(0,t2)
Discrete Uniform Distribution - Concept and Example
Discrete Uniform Distribution - Probability Mass Function PMF
Discrete Uniform Distribution - Cumulative Distribution Function CDF
Discrete Uniform Distribution - Derivation of the Mean and Variance
Discrete Uniform Distribution - Derivation of the MGF
Binomial Distribution - Binomial experiment and PMF
Binomial Distribution – Example
Binomial Distribution - Shape of the distribution
Binomial Distribution - Another Example
Binomial Distribution - Mean and Variance with example
Binomial Distribution - Derivation of the MGF
Binomial Distribution - Recognizing the parameters by its MGF
Binomial Distribution - The sum of m independent Binomial random variables with identical p is also Binomial
Negative Binomial Distribution PMF and shape of the distribution
Negative Binomial Distribution - Application and Example
Geometric Distribution - PMF and shape of the distribution
Geometric Distribution - Application and example
Geometric Distribution - Mean and Variance with example
Multinomial Distribution
Multinomial Distribution - Binomial as a Special Case
Multinomial distribution - Application and example
Multinomial Distribution - MGF of the Trinomial Distribution as a special case of the Multinomial Distribution
Hypergeometric Distribution - PMF and shape of the distribution
Hypergeometric Distribution – Example
Hypergeometric Distribution - Derivation of the Mean
Hypergeometric Distribution - Derivation of the Variance
Poisson Distribution - PMF and shape of the distribution
Poisson Distribution - Poisson Process
Poisson Distribution - Poisson Process - Application and example
Poisson Distribution - Mean, Variance and Coefficient of Variation with example
Poisson Distribution - Derivation of Mean
Poisson Distribution - Derivation of Variance
Poisson Distribution – MGF
Poisson Distribution - Poisson Approximation to the Binomial distribution - Derivation
Poisson Distribution - Poisson Approximation to the Binomial distribution - Example
Continuous Uniform Distribution / Rectangular Distribution - PDF, CDF and shape of the distribution
Continuous Uniform Distribution - Derivation of Mean and Variance
Continuous Uniform Distribution - Application and example
Exponential Distribution - PDF, CDF and shape of the distribution
Exponential Distribution - Derivation of mean
Exponential Distribution - Derivation of variance
Exponential Distribution - Application and example
Exponential Distribution - Moment Generating Function MGF
Gamma Distribution - PDF, CDF and shape of the distribution
Gamma Distribution - Derivation of Mean and Variance
Gamma Distribution - computation of probabilities with an Example
Gamma Distribution - Moment Generating Function MGF
Beta Distribution - PDF, CDF and shape of the distribution
Beta Distribution - Derivation of Mean and Variance
Beta distribution - Application and example
Normal Distribution - PDF, CDF and shape of the distribution
Normal Distribution - Standard normal random variable - Concept and its PDF
Normal Distribution - Process of Standardization, Area Table of the Standard Normal Distribution
Normal Distribution - Computation of some specific percentiles
Normal Distribution - Function f(x) of normal distribution is a proper PDF
Normal Distribution - Derivation of Mean and Variance
Normal distribution - Relationship between Mean, Median and Mode
Normal Distribution - Relationship between Quartile Deviation and Standard Deviation
Normal Distribution - Points of Inflection of Normal curve
Normal Distribution - Odd order moments about the mean
Normal Distribution - Even order moments about the mean
Normal Distribution - Obtaining the first two Raw Moments from its MGF
Normal Distribution - Cumulant Generating Function and its utilization for finding its cumulants
Normal Distribution - Normal Approximation to the Binomial distribution
Normal Distribution - Normal Approximation to the Poisson distribution
Bivariate Normal Distribution - PDF and shape of the distribution
Bivariate Normal Distribution - Detailed Discussion of the Shape of the Distribution
Bivariate Normal Distribution - Computation of probabilities with an example
Bivariate Normal Distribution - Moment Generating Function MGF
Bivariate Normal Distribution - Marginal Distributions are themselves Normal
Bivariate Normal Distribution - X and Y are independent IF AND ONLY IF the Correlation Coefficient ? = 0
Bivariate Normal Distribution - Conditional Distributions are themselves Normal
Bivariate Normal Distribution - Conditional Distributions are themselves Normal - Graphical Interpretation
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