A stockroom currently has 30 components of a certain type, of which 8 were provided by supplier 1, 10 by supplier 2, and 12 by supplier 3. Six of these are to be randomly selected for a particular assembly. Let X be the number of supplier 1’s components selected, Y be the number of supplier 2’s components selected. Find the following: a. joint pmf of X and Y b. the marginal distributions c. the conditional distributions

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A stockroom currently has 30 components of a certain type, of which 8 were provided by supplier 1, 10 by supplier 2, and 12 by supplier 3. Six of these are to be randomly selected for a particular assembly. Let X be the number of supplier 1’s components selected, Y be the number of supplier 2’s components selected.

Find the following:

a. joint pmf of X and Y

b. the marginal distributions

c. the conditional distributions

d. the conditional expectations, E[X | Y=y] 

e. Cov(X,Y)

 

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