Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows:

a. Find the marginal probability mass function px (x).

b. Find the marginal probability mass function py (y).

c. Find μx.

d. Find μy.

e. Find σx.

f. Find σy.

g. Find Cov(X, Y).

h. Find ρx,y.

Solution:

Step 1 of 5:

Automobile engines and transmissions are produced on assembly lines,they are inspected for defects. Those with defects are repaired. If X be the number of engines, and Y be the number of transmissions that require repairs in a one hour time interval.The joint probability of X and Y are given as

Y | |||||

X 0 1 2 3 | |||||

0 |
0.13 |
0.10 |
0.07 |
0.03 |
0.33 |

1 |
0.12 |
0.16 |
0.08 |
0.04 |
0.40 |

2 |
0.02 |
0.06 |
0.08 |
0.04 |
0.20 |

3 |
0.01 |
0.02 |
0.02 |
0.02 |
0.07 |

0.28 |
0.34 |
0.25 |
0.13 |

We have to find

- The marginal probability mass function
- The marginal probability mass function

- cov(X,Y)