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In a piston assembly, the specifications for the clearance
Chapter 2, Problem 4E(choose chapter or problem)
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below:
a. Find the marginal probability mass function of X.
b. Find the marginal probability mass function of Y.
c. Are X and Y independent? Explain.
d. Find \(\mu_{X}\) and \(\mu_{Y}\).
e. Find \(\sigma_{X}\) and \(\sigma_{Y}\).
f. Find Cov(X, Y)
g. Find \(\rho(X,\ Y)\).
Questions & Answers
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QUESTION:
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below:
a. Find the marginal probability mass function of X.
b. Find the marginal probability mass function of Y.
c. Are X and Y independent? Explain.
d. Find \(\mu_{X}\) and \(\mu_{Y}\).
e. Find \(\sigma_{X}\) and \(\sigma_{Y}\).
f. Find Cov(X, Y)
g. Find \(\rho(X,\ Y)\).
ANSWER:Step 1 of 8
Given, the number with too little clearance is X and
The number with too much clearance is Y.
Then the joint probability mass function of X and Y is given in the table below.
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