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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?

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    The assertion a) contradicts b), which is correct.2012-10-16
  • 0
    ($I_A +I_B)^2=I^2_A +2 I_A I_B + I^2_B$, so this RV takes values 0, 1 and 4. Besides 'describe the distribution' is quite vague2012-10-16

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