Exercise 4.1 The number of defects on the front side (X) of a wooden panel and thenumber 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 asfx (x, y) = s(x +y), x = 1, 2, 3 and y = 1, 2, 3Determine the value of c.2. Determine the marginal p.m.f. of X. Find also the mean and varianceof X.3. Determine the conditional p.mf of Y given X= 2. Find also theconditional mean and conditional variance of Y given X= 2.4. Check if the number of defects on the front side (X) of a wooden paneland the number of defects on the rear side (Y) of the panel areindependent.Exercise 4.2 In the transmission of digital information, the probabilities that a bit hashigh, moderate, and low distortion are 0.01, 0.04, and 0.95, respectively. Supposethat n = 5 bits are transmitted and the amount of distortion of each bit isindependent.1. Find the probability that one bit has high distortion, one has moderatedistortion, and three bits have low distortion.2. Find the probability that four bits have low distortion.Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness ofa paper product. Let X and Y denote the measurements of each of the twomethods.1. Suppose that the joint p.d.f of X and Y is modeled byfox (x, y) = c, 0

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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 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.mf 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

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 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.mf 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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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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
fx (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 p.mf 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 4.2 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.
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
fox (x, y) = c, 0<x<4,0<y and x - 1<y<x+1
Determine the value of c.
2. Determine the marginal probability distribution of X. Find also the
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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