Jet Copies

Monique Moore

Quantitative Methods – MAT 540

Dr. Vargha Azad

Jet Copies Case Problem

1) For generating the number of days needed to repair the copier, we need to graphic the cumulative distribution of repair times. The cumulative distribution and random number ranges for the distribution of repair times are shown in the following table.

|Repair time (y) |P(y) |Cumulative |Random Number Ranges|

|Days | |Probability | |

|1 |0.2 |0.2 |0.01 - 0.20 |

|2 |0.45 |0.65 |0.21 - 0.65 |

|3 |0.25 |0.9 |0.66 - 0.90 |

|4 |0.1 |1 |0.91 - 0.99 |

For generating the repair times using the above distribution, we generate a random number r from 0 to 1. If the random number lies between 0.01 and 0.20, the repair time is 1 day, if it is between 0.21 and 0.65, the repair time is 2 days, if it lies between 0.66 and 0.90, the repair time is 3 days and if it is between 0.91 and 0.99, we take the repair time as 4 days. But in doing the calculations, none of the random numbers went pass 0.99.

2) Here it is given that the time between breakdowns was probably between 0 and 6 weeks, with the probability increasing the longer the copier went without breaking down. So, if we define the random variable x as the time between breakdowns, its probability function will be of the form

[pic]

By computing the area under the curve [pic] from 0 to any value of the random variable x, we can determine the cumulative probability function of the random variable x as follows

[pic].

Cumulative probabilities are similar to the discrete ranges of random numbers generated in the above table for simulating the numbers of days needed to repair the copier. So, we can simulate the random variable x using a random number [pic] using the relationship,

[pic]...