Refer to Exercise 4. Assume that the cost of repairing an assembly whose clearance is too little is $2, and the cost of repairing an assembly whose clearance is too much is $3.

a. Express the total cost of repairs in terms of X and Y.

b. Find the mean of the total cost of repairs.

c. Find the standard deviation of the total cost of repairs.

Step 1 of 4:

Here,it is given that X be the number with too little clearance and Y be the number with too much clearance.

The cost of repairing X is $2 and cost of repairing Y is $3.

Also the joint probability mass function of X and Y is given as

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 |

Using these,we have to find the required values.

Step 2 of 4:

Here we have to express the total cost of repair in terms of X and Y.

Total cost of repair can be expressed as 2X+3Y.

Thus,total cost of repair is 2X+3Y.