TIFR ECE 2018 | Question: 9

Question

Let $X$ and $Y$ be two independent and identically distributed binary random variables that take values $\{-1,+1\}$ each with probability $1 / 2$. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Consider the following statements.

1. $Z_{1}$ and $Z_{2}$ are uncorrelated
2. $Z_{1}$ and $Z_{2}$ are independent
3. $P\left(Z_{1}=Z_{2}\right)=\frac{1}{2}$

Which of the above statements is/are $\text{TRUE}?$

• A. Only $\text{(i)}$
• B. Only $\text{(ii)}$
• C. Only $\text{(iii)}$
• D. Both $\text{(i) and (ii), but not (iii)}$
• E. All of $\text{(i), (ii) and (iii)}$