A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in?) and additive concentration is Tensile Strength Concentration of Additive 100 150 200 0.11 0.02 0.05 0.06 0.04 0.01 0.08 0.10 0.17 0.06 0.04 0.08 0.08 0.04 0.14 0.12 What are the marginal probability mass functions for X (additive concentration) and Y (tensile strength)? Are X and Y independent? Explain. a. b. Given that a specimen has an additive concentration of 0.04, what is the probability that its strength is 150 or more? Given that a specimen has an additive concentration of 0.08, what is the probability that its tensile strength is greater than 125? A certain application calls for the tensile strength to be 175 or more. What additive concentration should be used to make the probability of meeting this specification the greatest? C. d. e.

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A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint
probability mass function of tensile strength (in thousands of pounds/in?) and additive
concentration is
Tensile Strength
Concentration of Additive
100
150
200
0.11
0.02
0.05
0.06
0.04
0.01
0.08
0.10
0.17
0.06
0.04
0.08
0.08
0.04
0.14
0.12
What are the marginal probability mass functions for X (additive concentration) and Y
(tensile strength)?
Are X and Y independent? Explain.
a.
b.
Given that a specimen has an additive concentration of 0.04, what is the probability
that its strength is 150 or more?
Given that a specimen has an additive concentration of 0.08, what is the probability
that its tensile strength is greater than 125?
A certain application calls for the tensile strength to be 175 or more. What additive
concentration should be used to make the probability of meeting this specification the
greatest?
C.
d.
e.
Transcribed Image Text:A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in?) and additive concentration is Tensile Strength Concentration of Additive 100 150 200 0.11 0.02 0.05 0.06 0.04 0.01 0.08 0.10 0.17 0.06 0.04 0.08 0.08 0.04 0.14 0.12 What are the marginal probability mass functions for X (additive concentration) and Y (tensile strength)? Are X and Y independent? Explain. a. b. Given that a specimen has an additive concentration of 0.04, what is the probability that its strength is 150 or more? Given that a specimen has an additive concentration of 0.08, what is the probability that its tensile strength is greater than 125? A certain application calls for the tensile strength to be 175 or more. What additive concentration should be used to make the probability of meeting this specification the greatest? C. d. e.
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