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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 f (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.m.f of X and Y is modeled as f (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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer the following problems showing complete solution. Enclose finals answers. ELABORATE 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) = <(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 4.2 In the transmission of digital information, the probabilities that a bit has high, moderate, and low distortion are 0.01, 0.04, and 0.95, respectively. Suppose that n = 5 bits are transmitted and the amount of distortion of each bit is independent. 1. Find the probability that one bit has high distortion, one has moderate distortion, and three bits have low distortion. 2. Find the probability that four bits have low distortion. nd for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or ronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibit 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 andx - 1 <y<x+1 Determine the value of c. 2. Determine the marginal probability distribution of X. Find also the Engr. A. CUH-ING 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:Answer the following problems showing complete solution. Enclose finals answers. ELABORATE 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) = <(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 4.2 In the transmission of digital information, the probabilities that a bit has high, moderate, and low distortion are 0.01, 0.04, and 0.95, respectively. Suppose that n = 5 bits are transmitted and the amount of distortion of each bit is independent. 1. Find the probability that one bit has high distortion, one has moderate distortion, and three bits have low distortion. 2. Find the probability that four bits have low distortion. nd for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or ronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibit 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 andx - 1 <y<x+1 Determine the value of c. 2. Determine the marginal probability distribution of X. Find also the Engr. A. CUH-ING 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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