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 Icirc frac14 X and Icirc frac14 Y e Find Iuml X and Iuml Y f Find Cov(X, Y) g Find Iuml (X, Y) y 0 15 0 12 0 11 0 10 0 07 0 09 0 05 0 04 2 0 06 0 05 0 04 0 02 3 0 03 0 04 0 02 0 01 3

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

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:

y 0.15 0.12 0.11 0.10 0.07 0.09 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.03 0.04 0.02 0.01 3.

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 Î¼_X and Î¼_Y.

e. Find Ïƒ_X and Ïƒ_Y.

f. Find Cov(X, Y).

g. Find Ï(X, Y).

y 0.15 0.12 0.11 0.10 0.07 0.09 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.03 0.04 0.02 0.01 3.

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