# Homework Help: 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

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?)