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 fo (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
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 fo (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
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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
fo (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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0e78bad-15a7-452e-ae01-916ffff9d32e%2Fc4ef8b05-d604-4bae-ab58-571128b0ccf8%2Fdgcd71l_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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
fo (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.
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