Question

A stockroom currently has 30 components of a certain type, of which 12 components are provided by supplier 1, 7 components by supplier 2, and 11 components by supplier 3. 6 of these are to be selected for a particular assembly. X is a random variable representing the number of supplier 1's components that are selected and Y be the number of supplier 2's components that are selected.

(A) What is p(3,2)

(B) Using the logic of part (A), Obtain p(x,y). (This can be thought of as a multivariate hypergeometric distribution - sampling without replacement from a finite population consisting of more than 2 categories.

p (x,y)	1	2	3	4	5	6
1
2
3
4
5
6

NOTE: I already have answer for A which is 0.08559, I only need answers for B. Thank you!

Answer 1

form multinomial distribution:

P(x,y)=C(12,x)*C(7,y)*C(11,6-x-y)/C(30,6)

B)

p(x,y)	0	1	2	3	4	5	6
0	0.00078	0.00934	0.03668	0.06113	0.04585	0.01467	0.00156
1	0.00545	0.04668	0.12838	0.14265	0.06419	0.00934	0.00000
2	0.01167	0.07003	0.12838	0.08559	0.01751	0.00000	0.00000
3	0.00973	0.03890	0.04279	0.01297	0.00000	0.00000	0.00000
4	0.00324	0.00778	0.00389	0.00000	0.00000	0.00000	0.00000
5	0.00039	0.00042	0.00000	0.00000	0.00000	0.00000	0.00000
6	0.00001	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000