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 


x 
0 
1 
2 
3 
0 
0.15 
0.12 
0.11 
0.10 
1 
0.09 
0.07 
0.05 
0.04 
2 
0.06 
0.05 
0.04 
0.02 
3 
0.04 
0.03 
0.02 
0.01 
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 7:
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.
y  
x  0  1  2  3 
0  0.15  0.12  0.11  0.1 
1  0.09  0.07  0.05  0.04 
2  0.06  0.05  0.04  0.02 
3  0.04  0.03  0.02  0.01 
Our goal is:
a). Find the probability mass function of X.
b). Find the probability mass function of Y.
c). Are X and Y are not independent? Explain.
d). Find mean and .
e). Find .
f). Find Cov (X,Y).
g). Find .
a).
Now we have to find the probability mass function of X.
Here we are summing all the rows to find a probability mass function.
Then...