Question

Three fair die are rolled. Use Monte Carlo simulation to estimate the probability distribution of the maximum of the three rolled die (i.e., let X represent the maximum when three fair die are rolled. Estimate p(X=i) for i= 1 to 6.). Simulate 10,000 times (10,000 replications/trials). Turn in a copy of the forecast frequency chart.

please show screenshots of how to do it on Crystal ball.

Answer 1

ANSWER::

We first generate 3 sets of  random integers 1,2,..,6 with equal probability and extract the maximum. Repeating the process 10000 times, we prepare a table with relative frequencies and plot them. The relative frequency table gives an estimate of the actual distribution.

i 1 2 3 4 5 6
P(X=i) 0.0038 0.0314 0.0878 0.1737 0.2879 0.4154

For query, comment.

R Program

nsim=10000
x=numeric(nsim)
for(i in 1:nsim)
{
x[i]=max(sample(1:6,3,replace=TRUE))
}
y=prop.table(table(x))
y
plot(y,ylab="Relative frequency")

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