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 fo (x, y) = c, 0
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 fo (x, y) = c, 0
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Transcribed Image Text: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.fof 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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