DSC 3120 Generalized Modeling Techniques with Applications

DSC 3120 Generalized Modeling Techniques with Applications

Sample Quiz 4

Solutions are shown highlighted in Yellow

1. Consider the following simulation of a coin toss, with the experiment performed 3 times.

AVERAGE = 11/3=3.66

______

a)Fill in the blanks in the table above. Write the rule you used in the space below.

If the random number is greater than 0.5, then I called it "Heads", else "Tails"

b)"All random numbers greater than 0.75 will be called Heads". What is wrong with the preceding rule as it applies to a coin toss simulation? Circle the correct response.

i)There will be too many "Heads" generated in the long run.

ii)There will be 75% "Tails", in the long run.

iii)The number of "Heads" will be 75% of all outcomes, in the long run.

iv)There is nothing wrong with the rule, if it is truly a fair coin.

Answer: ii) There will be 75% "Tails", in the long run. This is because the rule says that numbers from 0 to 0.75 will be tails and above .75 will be heads, so the proportion of tails to heads is 75 to 25.

c)The RAND() function in Excel generates random numbers that range from ______to ______, with a ______distribution.

From 0 to 1, with a Uniform (Even) distribution.

1. Consider the following demand pattern for a product for the past 50 weeks.

Fill in the blanks in the table so that using the last two columns for a VLOOKUP statement will let you map random numbers to the correct demand level.

Note that by starting with 0 in the Cum. Prob. Column and shifting the demand numbers up one row compared to the first column, it ensures that the VLOOKUP statement will work right. That is, all random numbers from 0 to 0.22 can be assigned to the demand level of 18, and so forth.

1. The following table shows a portion of a simulation for a queuing system involving trucks. Fill in the blanks for truck numbers 8 and 10. The blank boxes have been highlighted.

1. To simulate a discrete variable, why do we compute cumulative probabilities?

Because cumulative probs. range from 0 to 1, just like the random numbers that are generated in Excel, and thus the probs. give us the cutoff points for mapping the variable values to the random numbers.

1. Excel exercise (for your understanding, not for quiz)

• Simulate a variable that has the following distribution

Generate some random numbers. Find the cumulative probs. for the above variable, and use those as the cutoffs to map the random numbers generated to the values of the variable.

• Simulate a queuing system (single server, single queue) with an average arrival interval of 5 seconds and average service time of 3 seconds.

This is an exact replica of the queuing example on the web, with only the arrival interval and service time averages changing.