Re: Can you help me and Solve the equation ???

On May 16, 3:55 pm, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
The Qurqirish Dragon <qurqiri...@xxxxxxx> writes:

On May 16, 7:06 am, math_ali <math_...@xxxxxxxxx> wrote:
If I have that equation
A=D^2
and A must be positive integer
what is the probable value of D ???

Since you say the "probable" value of D, I am guessing that this is a
probability problem. That said, we need a probability distribution on
A to determine anything about D, other than the obvious (that D is the
positive or negative square-root of a positive integer). If A is
chosen uniformly at random from the positive integers, then all
possible values of D are equally likely (and the probability is
infinitesimal).

There is no such thing as "uniformly at random from the positive
integers".

True. I shouldn't have phrased it that way. I'm not certain how I
should have (since the construct is impossible to begin with). Maybe I
should have just said without a probability distribution on A, nothing
more can be said.

If, for example, we say A is chosen by rolling two standard 6-sided
dice, then there are 22 possible values for D, with the positive and
negative square roots of 7 being most likely, at 1/12 each.

Why should the positive and negative square roots be equally likely?

They shouldn't necessarily be so, but the best you can hope for with
no information on the distribution of a finite set of possibilities is
equal likelihood.
The two possible D's for any given A occur with probabilities p and 1-
p, but unfortunately p is unknown. It is akin to a coin flip, where if
you do not know the coin is unfair, then you can't do better than
assuming it is (until you flip it enough times for creating a
confidence interval and doing the appropriate analysis. Of course,
even then you have the problem that rare events do happen.)

If you are looking for the expected value of D, then it is 0
(regardless of the distribution of A). See if you can figure out why.
(one-word hint: symmetry)

Nonsense. It could be anywhere from +sqrt(E[A]) to -sqrt(E[A]).
The probability distribution of D is not determined by the probability
distribution of A.

If you allow me the explanation above of why the positive and negative
values for D can be assumed equally likely, then my expected value
statement holds due to a symmetry argument. If not, then I agree with
your statement of the possible range of values.
Note that I never even implied the distribution of D was determined by
that of A. In fact, I explicitly said "regardless of the distribution
of A."

.

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