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...
