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Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurements of each of the two methods. 1. Suppose that the joint p.dfof X and Y is modeled by fox (x, y) = c, 0

Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurements of each of the two methods. 1. Suppose that the joint p.dfof X and Y is modeled by fox (x, y) = c, 0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurements of each of the two methods. 1. Suppose that the joint p.d.f of X and Y is modeled by fx (x, y) = c, 0<x< 4,0 <y and x - 1 <y<x+1 Determine the value of c. 2. Determine the marginal probability distribution of X. Find also the mean and variance of X. 3. Determine the conditional probability distribution of Y given X= 2. Find also the conditional mean and conditional variance of Y given X= 2. 4. Check if the measurements of the two methods X and Y are independent.
Transcribed Image Text:Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurements of each of the two methods. 1. Suppose that the joint p.d.f of X and Y is modeled by fx (x, y) = c, 0<x< 4,0 <y and x - 1 <y<x+1 Determine the value of c. 2. Determine the marginal probability distribution of X. Find also the mean and variance of X. 3. Determine the conditional probability distribution of Y given X= 2. Find also the conditional mean and conditional variance of Y given X= 2. 4. Check if the measurements of the two methods X and Y are independent.
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