Calculating Value of "a" for Independent X,Y Variables

[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 necessary to calculate C)

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

 

[Ray Vickson]

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 necessary to calculate C)

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

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.

 

[ParisSpart]

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

 

[tiny-tim]

Parispart, follow the advice …

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.

 

[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'

 

[haruspex]

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'

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?

 

[tiny-tim]

Hi ParisSpart!

(just got up :zzz:)

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'

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?)