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Linear Algebra for MATH 308
Lecture 1: Vectors, Linear Independence, and Spanning Sets
Lecture 2: Operations with Matrices and Vectors
Lecture 3: Systems of Equations
Lecture 4: Determinant
Lecture 5: Eigenvectors and Eigenvalues
Lecture 6: Matrix Inverses and Diagonalization
Lecture 7: Systems of Differential Equations
Lecture 8: Systems of Differential Equations
Quantitative Finance
Several Variables Calculus
Section 1: Functions of Several Variables
Section 2: Limits and Continuity
Section 3: Partial Derivatives
Section 4: Tangent Planes and Linear Approximations
Section 5: The Chain Rule
Section 6: Directional Derivatives and the Gradient Vector
Section 7: Maximum and Minimum Values
Section 8: Lagrange Multipliers
Differential Equations
Section 1: Integrating Factor
Section 2: Separable Equations
Section 3: Compound Interest
Section 4: Variation of Parameters
Section 5: Systems of Ordinary Differential Equations
Section 6: Matrices
Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
Section 8: Homogeneous Linear Systems with Constant Coefficients
Section 9: Complex Eigenvalues
Section 10: Fundamental Matrices
Section 11: Repeated Eigenvalues
Section 12: Nonhomogeneous Linear Systems
Mathematical Probability
Section 1: Probabilistic Models and Probability Laws
Section 2: Conditional Probability, Bayes’ Rule, and Independence
Section 3: Discrete Random Variable, Probability Mass Function, and Cumulative Distribution Function
Section 4: Expectation, Variance, and Continuous Random Variables
Section 5: Discrete Distributions
Section 6: Continuous Distributions
Section 7: Joint Distribution Function, Marginal Probability Mass Function, and Uniform Distribution
Section 8: Independence of Two Random Variables, Covariance, and Correlation
Section 9: Conditional Distribution and Conditional Expectation
Section 10: Moment Generating Function
Section 11: Markov’s Inequality, Chebyshev’s Inequality, and Weak Law of Large Numbers
Section 12: Convergence and the Central Limit Theorem
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Section 9: Conditional Distribution and Conditional Expectation
Section 9: Conditional Distribution and Conditional Expectation
Instructions
This section covers the concepts listed below.
For each concept, there is a conceptual video explaining it followed by videos working through examples.
When you have finished the material below, you can go to the
next section
or return to the
main Mathematical Probability page
.
Concepts
Conditional Distribution
Conditional Expectation
Conditional Density Function
Links & Resources
Return to Mathematical Probability Page
Return to Mini-Course Main Page
Conditional Distribution
Watch Concepts Video
Examples
Directions:
The following examples cover the material from the video above.
Watch Example Video
Self-Assessment Questions
Directions:
The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
What is a conditional probability mass function?
Conditional Expectation
Watch Concepts Video 1
Watch Concepts Video 2
Watch Concepts Video 3
Examples
Directions:
The following examples cover the material from the video above.
Watch Example Video
Watch Example Video
Self-Assessment Questions
Directions:
The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
What is conditional expectation?
How do you define the conditional probability mass function \(X\) given \(Y=y\) in the discrete case? What about the corresponding conditional expectation?
How do you define the conditional probability density function of \(X\) given \(Y=y\) in the continuous case?
Conditional Density Function
Watch Concepts Video
Examples
Directions:
The following examples cover the material from the video above.
Watch Example Video
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