Calculating Mean Dice-Throw Values Over Time | Probabilities and Time Homework

[Niles]

Homework Statement

Hi all.

Say I roll a dice every 2 seconds. So in t seconds, I will have rolled the dice t/2 times. I want to find a way of knowing the mean value of the dice-throws (i.e. the mean number of eyes on the dice) as a function of the time t.

The Attempt at a Solution

Since there are equal probability of getting 1 .. 6, I would say the mean is just 3.5, and this is not dependent on time.


By the way, is there a difference between average and mean? The way I have understood it, the mean is the theoretical average of eyes when tossing the dice infinitely many times, while the average is looking at a specific series, i.e. the series 1, 3 and 5 has the average 3.

Thanks in advance.


Niles.

 

[HallsofIvy]

The mean is the "arithmetic average" for a uniform probability distribution as you have here or a "weighted average" if not. Your distinction is between the distribution mean and sample mean, not between "mean" and "average".

And, as you calculated, if you roll a die a number of times, the overall mean is a constant, 3.5. It is independent of the number of times you roll the die.

 

[Niles]

Thanks.