# Jet Copies Case Problems

**Topics:**Random variable, Cumulative distribution function, Probability distribution

**Pages:**3 (822 words)

**Published:**May 20, 2012

Lost revenue of Jet Copies due to breakdown can be done by generating random numbers from different probability distributions according the given probability law. The different steps of this simulation and assumption made are explained below. 1. Simulation for the repair time.

It is given that the repair time follows

|Repair Time (days) |Probability | |1 |0.2 | |2 |0.45 | |3 |0.25 | |4 |0.10 |

To generate a random number from the above distribution, we use the following procedure. Generate a random number denoted by r2 from between 0 and 1. If this generated random number is less than or equal to 0.2 take repair time = 1. If the generated random number is 0.2 to 0.65, we take repair time =2. If the generated random number is 0.65 to 0.90, we take repair time = 3 and take 4 otherwise. 2. Simulation for break-down Distribution

Given that the probability distributions of random variable X representing the time between break-downs varies from 0 to 6 weeks with probability increasing continuously, the copier went without breaking down can be approximated by the probability distribution

f(x) =x/180 < x < 6

Hence the distribution function of x is

F(x)=x2/360 < x < 6

If r1 is another random number generated between 0 and 1, then we can write

r1= x2/36

Hencex=6[pic]

Therefore to simulate from the break down distribution, generate a random number r1 between 0 and 1 and make the transformation, x=6[pic].

3. Simulation for Lost Revenue.

It is given that the number of copies sold per day follows a...

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