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. Suppose that the joint p.m.f of X and Y is modeled as fxy (x, y) = c(x+y), x=1, 2, 3 and y=1, 2, 3

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. Suppose that the joint p.m.f of X and Y is modeled as fxy (x, y) = c(x+y), x=1, 2, 3 and y=1, 2, 3

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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Question

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.

Suppose that the joint p.m.f of X and Y is modeled as fxy (x, y) = c(x+y), x=1, 2, 3 and y=1, 2, 3
Determine the value of c.
Determine the marginal p.m.f of X. Find also the mean and variance of X.
Determine the conditional p.m.f of Y given X=2. Find also the conditional mean and conditional variance of Y given X=2.
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.

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

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.
a. Suppose that the joint p.m.f of X and Y is modeled as fry (x, y) = c(x+y), x=1, 2, 3 and y=1, 2, 3
Determine the value of c.
b. Determine the marginal p.m.f of X. Find also the mean and variance of X.
c. Determine the conditional p.m.f of Y given X=2. Find also the conditional mean and conditional
variance of Y given X=2.
d. 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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