Question

Problem 10 Below is a working Matlab program to simulate many games of craps. The program plays 10,000 games, and determines Prob _win. Code this program and play 10,000 games 10 separate times. Make a table of P(win craps) with your ten results. How can you use this table to determine the accuracy of your game simulation % simulate the odds of winning at craps % CES 5010 clear num-10000 %number of simulations x=cei 1( rand (num ,4)*6); win-o try "help rand, and 'help ceil, to see what's happening for i=1 : num summ1 x (i,1)x (i,2) win win+1 else win win+l; end end end Prob winwin/num disp(l'Probability of winningnum2str (Prob win)])

Answer 1

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Get this output

We can use the 10 repetitions to get an average estimate of the probability of winning.

We can also get a 90% confidence interval (percentile interval as we will use percentiles, rather than standard error).

90% interval indicates that the significance level of $\alpha=1-90/100=0.1$

That means a 90% interval would be $[\alpha/2,1-\alpha/2]=[0.1/2,1-0.1/2]=[0.05,0.95]$

So 0.05 and 0.95 quantiles would be the 90% confidence interval for the winning probability.

From the output we can see that

• the average winning probability is 0.30315
• The 90% percentile interval for the winning probability is [0.2941,0.3098]. That is, we are 90% confident that the true winning probability lies between [0.2941,0.3098].