Refer to Exercise 4. The total number of assemblies that fail to meet specifications is X + Y.

a. Find μX+Y.

b. Find σX+Y.

c. Find P(X + Y = 3).

REFERENCE EXERCISE 4: 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 μX and μY.

e. Find σX and σY.

f. Find Cov(X, Y).

g. Find ρ(X, Y).

Step 1 of 4 :

Here the experiment is assembly of piston. X denotes the number with too little clearance and Y denotes the number with too much clearance.

Also,the joint probability mass of X and Y is given.

Using this we have to find the required values.