# Jet Copies

Topics: Random variable, Cumulative distribution function, Probability distribution Pages: 3 (923 words) Published: March 11, 2011
JET Copies Problem

The simulation of Jet Copies can be done by generating random numbers from given probability distributions. 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. .20

2. .45

3. .25

4. .10

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1.00

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 uniform probability distribution between 2,000 and 8,000 copies. The revenue loss random number per day can be obtained by generating a uniform random number r3 between 2000 and 8000. To get the lost business due to this break down is obtained by multiplying r3 by repair time and lost revenue is obtained by multiplying r3* repair...