A product is classified according to the number of defects it contains and the factory that produces it. Let X and Y be the random variables that represent the number of defects per unit (taking on possible values 0, 1, 2, or 3) and the factory number (taking on possible values 1 or 2), respectively. The entries in the table represent the joint probability mass function of a randomly chosen product. X p(x,y) 1 2 3 1 0.30 0.18 0.09 0.03 Y 2 0.20 0.12 0.06 0.02 a) Find the probability that there are less than 2 defects per unit. b) Find P(X– Y = 0)

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A product is classified according to the number of defects it contains and the
factory that produces it. Let X and Y be the random variables that represent the
number of defects per unit (taking on possible values 0, 1, 2, or 3) and the factory
number (taking on possible values 1 or 2), respectively. The entries in the table
represent the joint probability mass function of a randomly chosen product.
Question 1:
X
p(x,y)
1
2
3
1
0.30
0.18
0.09
0.03
Y
2
0.20
0.12
0.06
0.02
a) Find the probability that there are less than 2 defects per unit.
b) Find P(X– Y = 0).
c) Given factory 1 produced the unit, what is the probability that there are 2
defects per unit?
d) Find the covariance of X and Y.
e) Are X and Y independent? Support your answer appropriately.
Transcribed Image Text:A product is classified according to the number of defects it contains and the factory that produces it. Let X and Y be the random variables that represent the number of defects per unit (taking on possible values 0, 1, 2, or 3) and the factory number (taking on possible values 1 or 2), respectively. The entries in the table represent the joint probability mass function of a randomly chosen product. Question 1: X p(x,y) 1 2 3 1 0.30 0.18 0.09 0.03 Y 2 0.20 0.12 0.06 0.02 a) Find the probability that there are less than 2 defects per unit. b) Find P(X– Y = 0). c) Given factory 1 produced the unit, what is the probability that there are 2 defects per unit? d) Find the covariance of X and Y. e) Are X and Y independent? Support your answer appropriately.
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