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Suppose i have a discrete random variable A such that:

  • $p(A=-1) = 3/4$
  • $p(A=0) = 1/8$
  • $p(A=1) = 1/8$

Now, i create a random variable $B = |A|$ and so

  • $p(B=0)= 1/8$
  • $p(B=1)= 7/8$

I want to compute $f_{A,B}(a,b)$ [generalized joint probability density function, using delta dirac function since it is a discrete case].

Are those variables independent so can I do $f_{A,B}(a,b)=f_A(a)\cdot f_B(B)$? Or, if they are dependent, when calculating $P(a_i,b_n)$ should i do $P(a_i,b_n) = P(A=a_i)\cdot P(B=b_n\mid A=-1)$ just like in Bayes Theorem ?

Thanks in advance.

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This distribution is a sum of Dirac distributions at {-1,1}, {0,0} and {1,1}. Surely you can guess the weight at each point. –  Did Dec 7 '12 at 6:48
    
Didn't get it .. Are the random variables A and B independent ? –  user1843665 Dec 7 '12 at 6:51
    
1. Do you know the definition of some random variables being independent? 2. Can you compute P(A=1), P(B=0) and P(A=1,B=0)? 3. Ergo? –  Did Dec 7 '12 at 6:55
    
Yes, even tho what i'm interested in is the generalized joint probability density function.You said the sum of {-1,1}, {0,0} and {1,1} ( with proprer weigths and delta function ) equals fA,B(a,b) ? –  user1843665 Dec 7 '12 at 6:56
    
the generalized joint probability density function... Meaning? // You said the sum of {-1,1}, {0,0} and {1,1}... Nope, I did not say that (and I do not know what it is that you call the sum of {-1,1}, {0,0} and {1,1}). –  Did Dec 7 '12 at 14:52
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