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Exercise 4.1 The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. 1. Suppose that the joint p.mf of X and Y is modeled as fx (x, y) = c(x + y), x = 1, 2, 3 and y =1, 2, 3 Determine the value of c. 2. Determine the marginal p.m.f. of X. Find also the mean and variance of X. 3. Determine the conditional p.m.f. of Y given X= 2. Find also the conditional mean and conditional variance of Y given X = 2. 4. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent. Engr A CUH-ING

Exercise 4.1 The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. 1. Suppose that the joint p.mf of X and Y is modeled as fx (x, y) = c(x + y), x = 1, 2, 3 and y =1, 2, 3 Determine the value of c. 2. Determine the marginal p.m.f. of X. Find also the mean and variance of X. 3. Determine the conditional p.m.f. of Y given X= 2. Find also the conditional mean and conditional variance of Y given X = 2. 4. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent. Engr A CUH-ING

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 25EQ
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Exercise 4.1 The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. 1. Suppose that the joint p.m.f of X and Y is modeled as Ex (x, y) = <(x + y), x = 1, 2, 3 and y = 1, 2, 3 Determine the value of c. 2. Determine the marginal p.m.f. of X. Find also the mean and variance of X. 3. Determine the conditional p.m.f. of Y given X= 2. Find also the conditional mean and conditional variance of Y given X = 2. 4. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent. Engr. A. CUH-ING
Transcribed Image Text:Exercise 4.1 The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. 1. Suppose that the joint p.m.f of X and Y is modeled as Ex (x, y) = <(x + y), x = 1, 2, 3 and y = 1, 2, 3 Determine the value of c. 2. Determine the marginal p.m.f. of X. Find also the mean and variance of X. 3. Determine the conditional p.m.f. of Y given X= 2. Find also the conditional mean and conditional variance of Y given X = 2. 4. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent. Engr. A. CUH-ING
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