Relative Frequency Histograms and Probability Density Functions

Question

The function called DicePlot simulates rolling 10 dice 5000 times.

The function 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 where each bin in the histogram represents a possible value of for the sum of the dice.

The mean and standard deviation of the 1 ⇥ 5000 sums of dice values will be computed, and the probability density function of normal distribution (with the mean and standard deviation computed) on top of the relative frequency histogram will be plotted.

Below is my code so far - What am I doing wrong? The graph shows up but not the extra red line on top? I looked at answers like this, and I don't think I'll be plotting anything like the Gaussian function.

% 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)
Y = normpdf(X)
xlabel('sum of dice values')
ylabel('relative frequency')
title(['NumDice = ',num2str(NumDice),' , NumRolls = ',num2str(NumRolls)]); 
  end

It is supposed to look like

But it looks like

Answer 1

The red line is not there because you aren't plotting it. Look at the documentation for normpdf. It computes the pdf, it doesn't plot it. So you problem is how do you add this line to the plot. The answer to that problem is to google "matlab hold on".

Answer 2

Here's some code to get you going in the right direction:

% Normalize your distribution 
normalizedDist = distr/sum(distr);
bar(normalizedDist ,1); 
hold on

% Setup your density function using the mean and std of your sample data
mu   = mean(SumDice);
stdv = std(SumDice);
yy   = normpdf(xx,mu,stdv);
xx   = linspace(0,60);

% Plot pdf
h = plot(xx,yy,'r'); set(h,'linewidth',1.5);