GNE 331 – LAU – Package 2
August 30, 2021 2021-08-30 17:54GNE 331 – LAU – Package 2
GNE 331 – LAU – Package 2

In section 5, we learn more about the continuous random variables and their distributions: Uniform Distribution, Normal Distribution, Exponential Distribution, Gamma Distribution, and Chi-Squared Distribution. We also learn about how to go from one pdf to another.
In section 6, we learn about joint probability distributions of TWO random variables (both continuous and discrete). In this section, we cover important parameters such as conditional pdfs, conditional expectations, covariance, correlation, and independence of two random variables.
In section 7, we learn that sample statistics (such as sample mean and sample standard deviation) are random variables by themselves. We learn more about sampling distributions and how to calculate probabilities concerning sample statistics.
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Section 5: Continuous Probability Distributions
In this section we learn about various continuous probability distributions: Uniform , Normal , Exponential , Gamma, and Chi-squared distributions are fully explained.
- Lesson 1: Continuous Random Variables and Probability Density Functions
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Problem 1: pdf
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Lesson 2: Expected Value and Variance
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Lesson 3: Cumulative Distribution Function (cdf)
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Problem 2: Cumulative Distribution Function
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Quiz 1: pdfs and cdfs
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Quiz 1 Solution
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Lesson 4: Continuous Random Variables and Probability Density Functions
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Lesson 5: Uniform Distribution
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Lesson 6: Normal Distribution Curve
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Lesson 7: Standard Normal Distribution Curve
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Table 1: Standard Normal Table
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Lesson 8: From X to Z
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Quiz 2: Uniform and Normal Distributions
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Quiz 2 Solution
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Lesson 9: Exponential Distribution
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Lesson 10: The Memoryless Property of The Exponential Distribution
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Lesson 11: Exponentials in a Poisson Process
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Lesson 12: The Gamma Distribution
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Lesson 13: The Incomplete Gamma Function
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Table 2: Incomplete Gamma Function
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Quiz 3: Exponential and Gamma Distributions
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Quiz 3 Solution
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Lesson 14: The Chi-Squared Distribution
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Table: Chi-Squared Distribution
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Lesson 15: Approximating Binomial Distribution by Normal Distribution
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Quiz 4: Lessons 14 and 15
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Quiz 4 Solution
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Lesson 16: From One pdf to Another
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Quiz 5: From One Pdf to Another
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Quiz 5 Solution
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Section 6: Joint Probability Distributions
In this section , we expand our knowledge from a single random variable (continuous or discrete) to two random variables (continuous and discrete). We learn how to calculate probabilities, expected values, and correlation of two random variables.
- Lesson 1: Introduction to Joint Probability Distributions
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Lesson 2: Joint and Marginal pmf in Two Discrete Random Variables
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Lesson 3: Expected Value of a Function of Two Discrete Random Variables
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Lesson 4: Covariance and Linear Relationships
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Lesson 5: Correlation of Two Random Variables
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Lesson 6: Independence of Two Random Variables
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Quiz 1: Joint Probability Distribution (Discrete Case)
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Quiz 1 Solution
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Lesson 7: Introduction to Joint pdf in Two Continuous Random Variables
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Problem 1: Review On Double Integrals
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Problem 2: Review On Double Integrals
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Lesson 8: Marginal pdf in Two Continuous Random Variables
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Lesson 9: Expected Value of a Function of Two Continuous Random Variables
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Problem 3: Covariance and Correlation of Two Continuous Random Variables
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Problem 4: Independence of Continuous Random Variables
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Problem 5: Conditional Probability of Two Random Variables
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Problem 6: E(min(X,Y))
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Problem 7: E(absolute value)
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Quiz 2 – Joint Probability Distributions for Two Continuous Random Variables
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Quiz 2 Solutions
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Lesson 10: Conditional pmf/pdf
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Lesson 11: Conditional Expectation
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Lesson 12: Expected Value And Variance Of A Linear Combination
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Quiz 3 – Conditional Probability and Conditional Expectation
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Quiz 3 Solution
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Section 7: Fundamental Sampling Distributions
In this section we learn the fundamental sampling distributions of the sample mean, the sample proportion and the sample variance
- Lesson 1: Fundamental Sampling Distribution
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Lesson 2: Distribution Of The Sample Mean For Normal Distribution
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Lesson 3: Central Limit Theorem
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Lesson 4: Sampling Distribution of The Sample Proportion
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Lesson 5: Sampling Distribution of the Sample Variance
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Quiz – Sampling Distributions
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Quiz Solution