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:

Step 1 of 2

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 .