calculate the PMF of y (sum of three dices) and plot it

Hello

I pretty confused about how to calculate the PMF of sum of three dices (represented by y such as 3,4,5...18) and how to plot its PMF using Matlab.

I feel like we need to use hist function but have no idea where to start. Hope someone can help me figure out!

Answer 1

[Image Analyst]

Not sure what PMF is. Did you ever actually try histogram()?

numRolls = 1000000;
numDice = 3;
dieFaces = randi([1, 6], numRolls, numDice);
theSums = sum(dieFaces, 2);
histObject = histogram(theSums, 'Normalization','pdf')
grid on;
xlabel('Sums');
ylabel('PDF')

[Ee]

Thanks for the help first!

PMF in here is "probability mass function" for short. I am not sure what histogram exactly is, is it a way to plot PMF?

[Image Analyst]

Well you'd better read up on what a histogram is then. It's super important in so many fields. Basically it gives a frequency of occurrence of values in your data set. I don't know what PMF is but if it's the probability that a mass will take on a certain value then yes, the histogram (which is the probability distribution function of the mass) will give that to you.

[Ee]

appreciate!

could I know is there any way can plot the CDF (culmulative distribution function) of Y as well?

[Paul]

The histogram is only an estimate of the PMF. If you need an exact answer for the PMF you might want to consider an alternate approach. For example, running the code above

numRolls = 1000000;
numDice = 3;
dieFaces = randi([1, 6], numRolls, numDice);
theSums = sum(dieFaces, 2);
histObject = histogram(theSums, 'Normalization','pdf');
grid on;
xlabel('Sums');
ylabel('PDF')

Yields these answers for the probability that the sum of the dice = 3 and 18 respectively

format long e
histObject.Values(1)

ans = 
     4.631000000000000e-03

    histObject.Values(end)

ans = 
     4.645000000000000e-03

These values are close, but they are not the same, even though they should be. And neither is the same as the exact answer

1/6^3

ans = 
     4.629629629629629e-03

We wouldn't expect the two end outputs of histogram to be the same as each other, nor the same as the exact answer, because they are based on random data.

[Ee]

Thanks a lot for the explanation!

What is the way of ploting CDF?(culmulative distribution function) of x and Y?(Not the PMF above)

Let's say x can take on values in {1,2,3,4,5,6} and y still is the sum of three dices {3,4,...18}

[Paul]

One you know the PMF, for example from the Values of histObject above, the function

doc cumsum

would be of interest for computing the CDF. The functions

doc stem
doc stairs

would be of interest for plotting the CDF.

[Ee]

Thank you! I will try!