Probability of Multiple Tetrahedron Rolling Multiple Times

[Septim]

Greetings,

I have taken a probability course a year ago; however my mind is a bit rusty and I cannot recall the concepts. I want to be able to calculate the probability distribution function for the following question:

Suppose you have a tedrahedron with number 1,2,3,4 on respective faces. If you roll 10 such tetrahedrons 100 times, what will the mean value of the number and the variance we get. Plot the distribution as a function of number.

I think I can think of the outcomes as 10 tuples each having probabiliy (1/4)^10 and calculate the expectation value from this approach, yet I am not sure that this will work. Do you have any suggestions recommendations?

Thanks in advance

 

[Stephen Tashi]

what will the mean value of the number and the variance we get.

What number?

 

[Septim]

I will clarify it, but I think our instructor referred to the sum of all numbers in all cases.

 

[Stephen Tashi]

You should calculate the mean and variance for 1 throw the tetrahedron. Then use the theorems about the mean and variance of the sum of independent random variables.

You instructor may have meant the "the number" to be the sum of the faces obtained when 10 tetrahedrons are thrown.

 

[Septim]

Well thanks for your answers; I think that will definitely work out. Then I shall calculate it for 1 throw of 10 tetrahedrons first. Then 100 is the number of trials just like in the binomial distribution. Since we have a large number of trials we will expect some sort of a distribution. Did I get it right?

 

[Stephen Tashi]

You aren't using precise language and perhaps not using precise thinking. You should define the random variable whose mean and variance you want to calculate.

If X is a random variable then the sample mean of N independent realizations of X is another random variable , call it Y. It is true that Y has a distribution. It has a distribution regardless of whether N is a large or small number of trials. However since Y is expressible as a multiple of a sum of independent random realizations of X, you only need to know the mean and variance of X to find the mean and variance of Y. You should determine whether your instructors question is about a sample mean.

 

[Septim]

I apologize for the ambiguity raised. I have asked my instructor and he told me that he is concerned with the sum of all numbers that is 1000 numbers. He also remarked that each one is independent and I can think of the problem as 1000 throws of a single tetrahedron dice. Throw of a single tetrahedron has an expectation value of 2.5 and I should link this to qthe throw of 1000 tetrahedrons.