If $A$ and $B$ are independent, with indicator random variables $I_A$ and $I_B$. How can we describe the distribution of $(I_A + I_B)^2$ in terms of $P(A)$ and $P(B)$? I would think its sufficient to say:
a) it has 2 values, 0 or 1
b) has a maximum of 4 and minimum of 0
c) and that its expected value is $E((I_A)^2)+2E(I_AI_B)+E((I_B)^2)$ which is equal to $P(A)^2+2P(A)P(B)+P(B)^2$
Is there anything else I can say?