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.Suppose that the joint p.d.f of X and Y is modeled by fxy (x, y) = c, 0 <x <4, 0<y and x-1 < y <x+1 Determine the value of c.Determine the marginal probability distribution of X. Find also the mean and variance of X.Determine the conditional probability distribution of Y given X=2. Find also the conditional mean and conditional variance of Y given X=2Check if the measurements of the two methods X and Y are independent.* SHOW COMPLETE SOLUTION WITH GIVEN, REQUIRED, AND SOLUTION. SHOW TABLE OF ILLUSTRATIONS IF NECESSARY. Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paperproduct. Let X and Y denote the measurements of each of the two methods.a. Suppose that the joint p.d.f of X and Y is modeled byfxy (x, y) = c, 0

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Answered: Exercise 4.3 Two measurement methods…

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.

Suppose that the joint p.d.f of X and Y is modeled by
fxy (x, y) = c, 0 <x <4, 0<y and x-1 < y <x+1
Determine the value of c.
Determine the marginal probability distribution of X. Find also the mean and variance of X.
Determine the conditional probability distribution of Y given X=2. Find also the conditional mean and conditional variance of Y given X=2
Check if the measurements of the two methods X and Y are independent.

* SHOW COMPLETE SOLUTION WITH GIVEN, REQUIRED, AND SOLUTION. SHOW TABLE OF ILLUSTRATIONS IF NECESSARY.

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.
a. Suppose that the joint p.d.f of X and Y is modeled by
fxy (x, y) = c, 0 <x <4, 0<y and x-1 < y <x+1
Determine the value of c.
b. Determine the marginal probability distribution of X. Find also the mean and variance of X.
c. Determine the conditional probability distribution of Y given X=2. Find also the conditional mean and
conditional variance of Y given X=2
d. Check if the measurements of the two methods X and Y are independent.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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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. Suppose that the joint p.d.f of X and Y is modeled by fxy (x, y) = c, 0