Indepedent Variables

1. May 18, 2013

ParisSpart

we have X,Y variables and we have f(m,n)=P(X=m,Y=n)=C*((1/(a*m*n+15*m+11*n+8))^2)
for what value of a X,Y are indepedent? ( its not necessery to calculate C)

i know that f(m,n)=f(m)*f(n) if X,Y are independent but how i am gonna use this for calculate a?

2. May 18, 2013

Ray Vickson

Never write what you did: you are using the same symbol (f) to mean three different things in the same problem. Use three different names, such as f(m,n) = g(m) * h(n).

Anyway, you need to find a value of 'a' that makes the denominator factor into a function of n alone times a factor of m alone.

3. May 18, 2013

ParisSpart

i will estimate (a*m*n+15*m+11*n+8)^2) ? if i will do it i find 10 terms

4. May 18, 2013

tiny-tim

Parispart, follow the advice

5. May 18, 2013

ParisSpart

i understand that i have to find a factor of n times a factor of n but i try to think how to do it using the 'a'

6. May 19, 2013

haruspex

When you have found a, what do you think the factors will look like, in general terms? Can you write a generic form for those factors, using some other unknown constants?

7. May 19, 2013

tiny-tim

Hi ParisSpart!

(just got up :zzz:)
Hint: if it was 1/(amn + m + n + 1)2,

how would you choose a so you could factor that?

(and what would the factors be?)

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