Question

My function called DicePlot, simulates rolling 10 dice 5000 times. In the function, it calculates the sum of values of the 10 dice of each roll, which will be a 1 × 5000 vector, and plot relative frequency histogram with edges of bins being selected in the same manner where each bin in the histogram should represent a possible value of for the sum of the dice.

The mean and standard deviation are computed of the 1 × 5000 sums of dice values and the probability density function of normal distribution (with the mean and standard deviation that is computed) on top of the relative frequency histogram is plotted.

I have everything done, but i’m confused on how to plot the probability density function. any help is appreciated. thanks!

for reference the graph is supposed to look like!

function DicePlot ( throw_num, die_num )

throw_num=5000
die_num= 10

  throws = rand ( throw_num, die_num );

  throws = ceil ( 6 * throws );

  for i = die_num : die_num*6
    j = find ( score == i );
    y(i-die_num+1) = length ( j ) / throw_num;
  end 

  bar ( x, y )

  xlabel ( 'Score' )
  ylabel ( 'Estimated Probability' )


  score_ave = sum ( score(1:throw_num) ) / throw_num;
  score_var = var ( score );



  return
end

Answer 1

I’ve added to the code from my answer to your previous question to plot a scaled Gaussian pdf over the top of your histogram. The two key additions are as follows: 1) Use hold on and hold off to get the histogram and plot on the same figure. 2) Scale the output of normpdf to the appropriate size so it is on the same scale as the histogram.

One other thing, I can’t help but notice you haven’t incorporated the suggestions from my previous answer into your function yet. Any particular reason for this? I certainly will not +1 your question unless I can see evidence that you’ve incorporated the suggestions you’ve had in the past into your work! And now you’ve gone and made me sound like one of my high-school teachers! 🙂

%#Define the parameters
NumDice = 2;
NumFace = 6;
NumRoll = 500;

%#Generate the rolls and obtain the sum of the rolls
AllRoll = randi(NumFace, NumRoll, NumDice);
SumRoll = sum(AllRoll, 2);

%#Determine the bins for the histogram
Bins = (NumDice:NumFace * NumDice)';

%#Build the histogram
hist(SumRoll, Bins);
title(sprintf('Histogram generated from %d rolls of %d %d-sided dice', NumRoll, NumDice, NumFace));
xlabel(sprintf('Sum of %d dice', NumDice));
ylabel('Count');
hold on

%#Obtain the mean and standard deviation of the data
Mu = mean(SumRoll);
Sigma = sqrt(var(SumRoll));

%#Obtain the Gaussian function using 4 standard deviations on either side of Mu
LB = Mu - 4 * Sigma; UB = Mu + 4 * Sigma;
Partition = (LB:(UB - LB) / 100:UB)';
GaussianData = normpdf(Partition, Mu, Sigma);

%#Scale the Gaussian data so the size matches that of the histogram
GaussianData = NumRoll * GaussianData;

%Plot the Gaussian data
plot(Partition, GaussianData, '-r');
hold off

ps, if you didn’t know a priori that the histogram should be Gaussian (because of a central limit theorem), then you could also use ksdensity from the statistics toolbox to get the empirical density using a kernel function.