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Independence of Variables

 
 
Reply Thu 21 Feb, 2013 01:12 am
I have this problem that I am stuck on and I know I must be looking at it wrong but if someone could help me that would be great. are X1, and X2 independent?
p(x1,x2)= { 2/(n(n+1)), for x1= 1,2,...n and x2=1.2,...x1
0, otherwise

In order to find independence I just apply p(x1,x2)= px1(x1)px2(x2) for all x,y.
For some reason I am having trouble proving independence due to not being able to solve each summation. WHAT AM I DOING WRONG????
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Kolyo
 
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Reply Thu 21 Feb, 2013 04:39 pm
@kmsnyder,
In order to show they are NOT independent you only need to show that

p(x1,x2) Not Equal p(x1)p(x2) for some x1, x2.

You get to pick the x1 and x2.
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Kolyo
 
  1  
Reply Fri 22 Feb, 2013 04:38 pm
@kmsnyder,
For example:

P(X1 = 1, X2 = n) = 0
P(X1 = 1) = 2/(n(n+1))
P(X2 = n) = 2/(n(n+1))
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