ENGG40Probataistisfor Chapter 4:Further Topics on Random Variables Instructor:Shengyu Zhang
Instructor: Shengyu Zhang
Content Derived Distributions Covariance and Correlation ■ Conditional Expectation and Variance Revisited Transforms Sum of a Random Number of Independent Random variables
Content ◼ Derived Distributions ◼ Covariance and Correlation ◼ Conditional Expectation and Variance Revisited ◼ Transforms ◼ Sum of a Random Number of Independent Random Variables
more advanced topics We introduce methods that are useful in: 0 deriving the distribution of a function of one or multiple random variables; 0 dealing with the sum of independent random variables,including the case where the number of random variables is itself random; 口 quantifying the degree of dependence between two random variables
more advanced topics ◼ We introduce methods that are useful in: ❑ deriving the distribution of a function of one or multiple random variables; ❑ dealing with the sum of independent random variables, including the case where the number of random variables is itself random; ❑ quantifying the degree of dependence between two random variables
We'll introduce a number of tools transforms convolutions, We'll refine our understanding of the concept of conditional expectation
◼ We’ll introduce a number of tools ❑ transforms ❑ convolutions, ◼ We’ll refine our understanding of the concept of conditional expectation
Derived distributions ■ Consider functions Y=g(X)of a continuous random variable X. Question:Given the PDF of X,how to calculate the PDF of Y? Also called a derived distribution. The principal method for doing so is the following two-step approach
Derived distributions ◼ Consider functions 𝑌 = 𝑔(𝑋) of a continuous random variable 𝑋. ◼ Question: Given the PDF of 𝑋, how to calculate the PDF of 𝑌? ❑ Also called a derived distribution. ◼ The principal method for doing so is the following two-step approach