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 μ_X and μ_Y.

e. Find σ_X and σ_Y.

f. Find Cov(X, Y).

g. Find ρ(X, Y).

Transcribed Image Text:

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.