# Transformation of Discrete Random Variable

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 ?