In a piston assembly, the specifications for the clearance between piston rings and the

Chapter 2, Problem 4

(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 \(X \text { and } Y\) independent? Explain.

d. Find \(\mu_{X} \text { and } \mu_{Y}\).

e. Find \(\sigma_{X} \text { and } \sigma_{Y}\).

f. Find \(\operatorname{Cov}(X, Y)\).

g. Find \(\rho(X, Y)\).

Equation Transcription:

Text Transcription:

X { and  Y

\mu_{X}and  \mu_{Y}

\sigma_{X} and  \sigma_{Y}

Cov(X, Y)

\rho(X, Y)

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