ENGR 371 – Concordia – Package 2
August 30, 2021 20210830 17:55ENGR 371 – Concordia – Package 2
ENGR 371 – Concordia – 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 ChiSquared 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.

Section 5: Continuous Probability Distributions
In this section we learn about various continuous probability distributions: Uniform , Normal , Exponential , Gamma, and Chisquared distributions are fully explained.
 Lesson 1: Continuous Random Variables and Probability Density Functions

Problem 1: pdf

Lesson 2: Expected Value and Variance

Lesson 3: Cumulative Distribution Function (cdf)

Problem 2: Cumulative Distribution Function

Quiz 1: pdfs and cdfs

Quiz 1 Solution

Lesson 4: Continuous Random Variables and Probability Density Functions

Lesson 5: Uniform Distribution

Lesson 6: Normal Distribution Curve

Lesson 7: Standard Normal Distribution Curve

Table 1: Standard Normal Table

Lesson 8: From X to Z

Quiz 2: Uniform and Normal Distributions

Quiz 2 Solution

Lesson 9: Exponential Distribution

Lesson 10: The Memoryless Property of The Exponential Distribution

Lesson 11: Exponentials in a Poisson Process

Lesson 12: The Gamma Distribution

Lesson 13: The Incomplete Gamma Function

Table 2: Incomplete Gamma Function

Quiz 3: Exponential and Gamma Distributions

Quiz 3 Solution

Lesson 14: The ChiSquared Distribution

Table: ChiSquared Distribution

Lesson 15: Approximating Binomial Distribution by Normal Distribution

Quiz 4: Lessons 14 and 15

Quiz 4 Solution

Lesson 16: From One pdf to Another

Quiz 5: From One Pdf to Another

Quiz 5 Solution

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

Lesson 2: Joint and Marginal pmf in Two Discrete Random Variables

Lesson 3: Expected Value of a Function of Two Discrete Random Variables

Lesson 4: Covariance and Linear Relationships

Lesson 5: Correlation of Two Random Variables

Lesson 6: Independence of Two Random Variables

Quiz 1: Joint Probability Distribution (Discrete Case)

Quiz 1 Solution

Lesson 7: Introduction to Joint pdf in Two Continuous Random Variables

Problem 1: Review On Double Integrals

Problem 2: Review On Double Integrals

Lesson 8: Marginal pdf in Two Continuous Random Variables

Lesson 9: Expected Value of a Function of Two Continuous Random Variables

Problem 3: Covariance and Correlation of Two Continuous Random Variables

Problem 4: Independence of Continuous Random Variables

Problem 5: Conditional Probability of Two Random Variables

Problem 6: E(min(X,Y))

Problem 7: E(absolute value)

Quiz 2 – Joint Probability Distributions for Two Continuous Random Variables

Quiz 2 Solutions

Lesson 10: Conditional pmf/pdf

Lesson 11: Conditional Expectation

Lesson 12: Expected Value And Variance Of A Linear Combination

Quiz 3 – Conditional Probability and Conditional Expectation

Quiz 3 Solution

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

Lesson 2: Distribution Of The Sample Mean For Normal Distribution

Lesson 3: Central Limit Theorem

Lesson 4: Sampling Distribution of The Sample Proportion

Lesson 5: Sampling Distribution of the Sample Variance

Quiz – Sampling Distributions

Quiz Solution