Given a 2-wise hash function $\sigma: [d] \rightarrow \{-1,+1\}$, i.e., $\sigma(a)$ will map any positive integer $a\leq d$ into real number $-1$ or $+1$ with equal probability. Then how to calculate the expectation $E[\sigma(1)\sigma(2)\sigma(3)]$? Here is the definition for k-wise independent http://www.math.rutgers.edu/~sk1233/courses/topics-S13/lec5.pdf
Could someone write the detailed steps? since I am not very sure how to use the definition 2-wise. Many thanks.