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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

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.
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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.
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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