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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.fof X and Y is modeled as fx (x, y) = c(x + Determine the value of c. - y), x = 1, 2, 3 and y = 1, 2, 3 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.

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.fof X and Y is modeled as fx (x, y) = c(x + Determine the value of c. - y), x = 1, 2, 3 and y = 1, 2, 3 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.

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 4.1 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 fox (x, y) = s(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 R.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.
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 fox (x, y) = s(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 R.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.
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