  In this paper, we prove that most of the boolean functions, $f : \{-1,1\}^n
\rightarrow \{-1,1\}$ satisfy the Fourier Entropy Influence (FEI) Conjecture
due to Friedgut and Kalai (Proc. AMS'96). The conjecture says that the Entropy
of a boolean function is at most a constant times the Influence of the
function. The conjecture has been proven for families of functions of smaller
sizes. O'donnell, Wright and Zhou (ICALP'11) verified the conjecture for the
family of symmetric functions, whose size is $2^{n+1}$. They are in fact able
to prove the conjecture for the family of $d$-part symmetric functions for
constant $d$, the size of whose is $2^{O(n^d)}$. Also it is known that the
conjecture is true for a large fraction of polynomial sized DNFs (COLT'10).
Using elementary methods we prove that a random function with high probability
satisfies the conjecture with the constant as $(2 + \delta)$, for any constant
$\delta > 0$.
