1. Sep 28, 2008

### jnimagine

So, we were given simulations of histograms that has to do with rolling a certain number of dice consecutive times.
and these questions were given...
and I am soo lost as to how to approach these questions.

1. What is a reasonable numerical measure of the width of the distribution?
2. Comparing the first two possibilities should show that the width of the distribution does not depend on the number of times the sets of rolls is repeated. Comparing all the possibilities but the first shows that it does depend on the number of rolls n. How does the width of the distribution correlate with the number of rolls? Be both qualitative and at least semi-quantitative: if n is the number of rolls does the width vary as n, 1/n, the square root of n, one over the square root of n, …

and also, for gaussian distribution, what is the mathematical relationship between FWHM (full width at half the maximum) and the standard deviation?

2. Oct 4, 2008

### jnimagine

anyone...????

3. Oct 5, 2008

### HallsofIvy

Staff Emeritus

You are probably getting no response because what you wrote makes so little sense.

Which distribution? Each time you rolled the dice a certain number of times? What are you plotting horizontally on your histogram?

Comparing what "first two possibilities"?

Again, what "possiblities"? Do you mean each time you rolled a specific number of dice? What are the width and number of rolls for the second trial? What are the width and number of rolls for the second trial? And, of course, what are you plotting, or measuring, along the base of the histograms?

4. Oct 5, 2008

### jnimagine

This is an assignment for physics... and I never learned anything about this sorta thing in my life and we're not getting taught anything about it either...

1. Which distribution? Each time you rolled the dice a certain number of times? What are you plotting horizontally on your histogram?

number of rolls on the y-axis and fraction of sevens in the x-axis.
ex. graph shows 36 rolls repeated 4000 times, 72 rolls 500 times etc.

2. Comparing the first two possibilities should show that the width of the distribution does not depend on the number of times the sets of rolls is repeated.

Comparing what "first two possibilities"?
36 rolls repeated 4000 times
36 rolls repeated 1000 times

3. Comparing all the possibilities but the first shows that it does depend on the number of rolls n. How does the width of the distribution correlate with the number of rolls? Be both qualitative and at least semi-quantitative: if n is the number of rolls does the width vary as n, 1/n, the square root of n, one over the square root of n, …

Again, what "possiblities"? Do you mean each time you rolled a specific number of dice? What are the width and number of rolls for the second trial? What are the width and number of rolls for the second trial? And, of course, what are you plotting, or measuring, along the base of the histograms?

- possibilities:
36 rolls repeated 4000 times
36 rolls repeated 1000 times
72 rolls repeated 500 times
144 rolls repeated 250 times
180 rolls repeated 200 times
288 rolls repeated 125 times
360 rolls repeated 100 times

- width varies for all the different possibilites... it seems to get narrower as you go down the list

- base of the histogram is the fraction of sevens

and also, for gaussian distribution, what is the mathematical relationship between FWHM (full width at half the maximum) and the standard deviation?
This looks like a question about a given formula. Which formula?

-no, "To find this you determine where the number of data is one-half of the value of the maximum, i.e. where N(x) = A/2. There will be two such points for a bell shaped curve. Then the FWHM is the difference between the right hand side value and the left hand side value of x." That's all it said and the above question came up.