Hi, I think that all depends on the probability density function you want. For example, if you generate random numbers following a normal density function with 0 mean and standart deviagtion=1, then for any sigma, sigma*X + m will follow a normal density with mean=m and standard deviation=sigma. At the opposite X^2 will not follow a normal density function.

Maybe this document could be of help? http://www.sci.csueastbay.edu/~esuess/classes/Statistics_6401/Handouts/trans/TransUnif.pdf

Dear Peter,

It is more deeper than what you posted.

If it is just one number you generate noone could possible tell the difference. For telling the difference, see any function, an algorythm you need a row of numbers. One number does not really reveal the information.

By just looking at probability of the single number comparing the functions with which they are generated (that is the only difference you can tell):

1) 100 possiblities

2) 10 possiblities

3) 100 possibilites

... but by just looking at a single number... all you can say by knowing the possible patterns is what pattern it could fit.

That is brilliant, Sayyed. Thank you for sharing it.

Thank you Carmen, just you got the tip.

procedure 2 and 3 does not give you all possible numbers between 0-100.

Dear prof. Tayyari, As I said before, I need just one random number and the question rises from two dilemmas. First, if I need just one random variable can I choose procedures 2 or 3 instead of 1? Second,  how does the random number distribution function change if I need a series of random numbers while doing procedure 2 and 3?

Fit has nothing to do with probability the number has in certain functions... just to tell you. It is senseless to calculate the probability... but you can do so if you are bored enough.

If you have a value... like 73... than you know:

73 can be in 1 but not in 2 since 2 is the square root of it's number. 73 cannot be in 3 either because... it is simply not part of multiplication table.

To make it more easy: 2 is already part of 3. If a number is not in 3, it is neither part of 2.

The correct row is rather 1, 3, 2 ... a number has the smallest probability being part of 2... Their amount is: 101, 43, 11 (counting zero as a number too)

101 -> 100%

43 -> 42,5 %

11 -> 10,9 %

The square root has by far the worst chance to be found in nature... That is why sand is more often on this planet than flowers *lol*

You can only take the square root to test it... but it has to be a full square. It is not so much about 'length' then...

OOOOO

OOOOO

OOOOO

OOOOO

OOOOO

Balls *lol*

Otherwise it is irrational... and you don't want it to be irrational... not if you are nature.

Very good discussion. What about non-discrete (continuous) random numbers? Think about it.

http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm

They are not part of the order. They are 'accuracy'...

1 object, 2 objects

1.5 is already accuracy... 0.5 is the accuracy with which I devide the space between 1 and 2, how much 2 you have. Infinite irrational numbers is dependend from the accuracy with which you cut. Infinite is then already a property. It only makes sense if you compare things. Indeed irrational numbers are not part of the row. They are another row.

1.1 , 2.1 , 3.1 ... Only those you can put into a row for the sake of their sameness..

And then it makes sense to compare:

1,2,3 1.1 , 2.1 , 3.1

and say that the difference is 0.1

See... there is an infinite difference between a natural number and a irrational number when it comes to a property, like wholeness. But who defines what's whole? It's only a scale... The 1.1 can be as whole as the 1 in its own way.

That's good U_U Come to the dark side of science. Because that is what people call you then: A satanist. Although we are rather more magicians U_U Like in fullmetal alchemist maybe. Anyway: Don't breathe too much!!!! We don't have trees here!!!!!

P.S.: This is for Bob

You need all possibilities not just an squared number. So the first is correct

Seeing is probably most convincing.  Then generate your numbers using prescription 1, 2 and 3 (separately) and see the three histograms of so obtained results, also for continuous case.  If you prefer numbers rather than pictures then compute average values or medians of your results.  Note: the results may be very different if you use another random number generator, with non-uniform distribution of produced results (triangular, exponential, or still other).

Aw the aethernal question about "How much random must be the output of a randomizer?", "What is random enough?", or more sickening: "Is my random set of objects R E A L L Y random or is there a subtle, elusive regularity which escapes my obsessive scrutiny?"... OK, lets be practical, if after a reasonably high number of objects generated, your histogram gives "equiprobable" for each one, your random degree is acceptable, but if you have a tendence or tendences, of course not. If you increase to a GREAT number of objects generated via the same randomizer criterion and the tendence/es vanish, ok, the randomizer runs properly, because your previous statistics could simply be based on an insufficient number of cases. BUT If after a H U G E number of objects generated via this randomizer (continuous case!) the tendencies remain, your randomizer fails... It could sound stupid, but I cannot think about this problem in other terms. Of course in proper literature are described randomizer criteria that are extensively used, so, by using them, we could remain comfortably unworried about this almost metaphysical problem... Greets from Mendoza, Argentina. Gustavo.