Relative Frequency Histograms and Probability Density Functions

Hi, I'm writing a function which simulates rolling 10 dice 5000 times. In the

function,I find the sum of values of the 10 dice of each roll, which will be a

1X5000 vector, and plot relative frequency histogram. Also I have to compute mean

and standard deviation of the 1x 5000 sums of dice values, and plot the

probability density function of normal distribution on top of the relative

frequency histogram.

I've got most of the code down, such as finding the sums, and my graph is

correct in shape, but it's not a relative frequency histogram but instead just

counts the number of occurrences of a value on the y-axis. I'm not sure how to

fix this. I think I'll be able to find the mean and standard deviation to make

the prob density function but help is always appreciated.

    % function[]= DicePlot()
for roll=1:5000
    diceValues = randi(6,[1, 10]);
    SumDice(roll) = sum(diceValues);
end
distr=zeros(1,6*10);
for i = 10:60
    distr(i)=histc(SumDice,i);
end
bar(distr,1)
xlabel('sum of dice values')
ylabel('relative frequency')
title(['NumDice = ',num2str(NumDice),' , NumRolls = ',num2str(NumRolls)]); 
  end

Answer 1

[Image Analyst]

Is this homework, because your classmate just posted the same thing here: http://www.mathworks.com/matlabcentral/answers/54408-problems-with-graphing-my-histogram?

Just do

distr= hist(SumDice, numberOfBins); % No loop over i needed.
distr = distr / sum(distr);

to normalize by the number of counts in the distribution.

[SB]

Yes it is, and so numberOfBins is 50? The graph appears shifted all the way to the left (values are now showing up for sum as less than 10 somehow), so that doesn't seem to work. Also, for the mean, would it just be mean(SumDice(roll))? How would stdev work in this case?

[Image Analyst]

You have to figure out how many bins there are in advance. Like this:

numberOfRolls = 1e7;
numberOfPairsOfDice = 5;
randomIntegers = randi(6, [numberOfRolls, numberOfPairsOfDice * 2]);
SumOf5PairsOfDice = sum(randomIntegers, 2); % Sum across columns
minSum = min(SumOf5PairsOfDice)
maxSum = max(SumOf5PairsOfDice)
numberOfBins = maxSum - minSum + 1
[counts binCenters] = hist(SumOf5PairsOfDice, numberOfBins); % No loop over i needed.
counts = counts / sum(counts);
bar(binCenters, counts, 'BarWidth', 1);
grid on;
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

Yes, the mean would be that and the stddev would be std(SumOf5PairsOfDice) - basically just like the mean.