# How to see random distribution

• Aug 14th 2013, 01:32 PM
cloud
How to see random distribution
Hi,
I need your suggestions for my problem. Assume I have 100 bags. Of these 40 bags have 0 balls, 28 bags have 1 ball, 15 bags got 2 balls, and so on.
1. From these values how to see whether the distribution of balls in the bags is random or not?
2. How the values would look like, if the distribution is random?
What type of statistical method should I use to get the answers. Thanks for your time.
• Aug 14th 2013, 01:49 PM
Shakarri
Re: How to see random distribution
Are you wondering if the number of bags with X balls is random instead of the number of bags being related to the number of balls inside them?
• Aug 14th 2013, 01:58 PM
cloud
Re: How to see random distribution
Thanks for your reply. I would like to know whether the distribution of number of bags being related to the number of balls is random or not.
• Aug 14th 2013, 02:25 PM
HallsofIvy
Re: How to see random distribution
Quote:

Originally Posted by cloud
Hi,
I need your suggestions for my problem. Assume I have 100 bags. Of these 40 bags have 0 balls, 28 bags have 1 ball, 15 bags got 2 balls, and so on.

What does "and so on" mean here?

Quote:

1. From these values how to see whether the distribution of balls in the bags is random or not?
2. How the values would look like, if the distribution is random?
What type of statistical method should I use to get the answers. Thanks for your time.
• Aug 14th 2013, 02:38 PM
Shakarri
Re: How to see random distribution
1 more question. Did you pick 100 bags at random or are those 100 bags all the bags that exist? The way you say you "have" 100 bags makes it sound like you know the number of balls in the entire population of bags.
• Aug 14th 2013, 02:43 PM
cloud
Re: How to see random distribution
Hi Hallsoflvy,
and so on.... means the remaining bags have some numbers of balls within it.
I have 100 bags. Of these 40 bags have 0 balls, 28 bags have 1 ball, 15 bags got 2 balls, 7 bags have 3 balls, 5 bags have 4 balls, 3 bags have 5 balls and the remaining 2 bags have 6 ball.
The distribution is like this: Whether it is random or not?
#bags # balls
40 0
28 1
15 2
7 3
5 4
3 5
2 6
Thanks.
• Aug 14th 2013, 02:47 PM
cloud
Re: How to see random distribution
Hi Shakarri,
Yes! I know the total number of bags and balls.
• Aug 14th 2013, 03:39 PM
Shakarri
Re: How to see random distribution
This isn't really a statistics problem because your samples are exact values, there isn't an uncertainty when taking samples. You cannot know for sure that there is no relationship, you can only show that certain relationships don't exist.
Call the number of bags Y and the number of balls X

Because you have 7 groups the equation $Y=f(X)=a_1X^6+a_2X^5+a_3X^4+a_4X^3+a_5X^2+a_6X+a_7$ will fit the data exactly.
From your data you would get the equations f(0)=40, f(1)=28, f(2)=15, f(3)=7, f(4)=5, f(5)=3, f(6)=2 and you would have a set of 7 simultaneous equations to solve for a1 to a7
So there is 1 example of a possible relationship but you don't often get polynomials in the order of X^6 so you may think that this relationship is wrong. What you need to do is think up all the forms of equations which you suspect could exist and test each one. Relationships like:
Y=aX+b,
Y=aX2+bX+c
Y=aex+b
are found quite often so you can start with them. Just use 2 or 3 points to find the variables a, b and c and then check if the equation you derived fits the other data points. If none of your ideas for equations work then you can conclude that the distribution is random.
• Aug 15th 2013, 08:03 AM
cloud
Re: How to see random distribution
Thanks Shakarri. You have shown me a direction to go from here. I will go with your suggestions.
• Aug 15th 2013, 08:17 AM
HallsofIvy
Re: How to see random distribution
Quote:

Originally Posted by cloud
Hi Hallsoflvy,
and so on.... means the remaining bags have some numbers of balls within it.
I have 100 bags. Of these 40 bags have 0 balls, 28 bags have 1 ball, 15 bags got 2 balls, 7 bags have 3 balls, 5 bags have 4 balls, 3 bags have 5 balls and the remaining 2 bags have 6 ball.
The distribution is like this: Whether it is random or not?
#bags # balls
40 0
28 1
15 2
7 3
5 4
3 5
2 6
Thanks.

No! NO specific distribution of numbers is "random". "Random" refers to HOW the numbers are determined, not the set of numbers themselves.