  The Fourier-Entropy Influence (FEI) Conjecture states that for any Boolean
function $f:\{+1,-1\}^n \to \{+1,-1\}$, the Fourier entropy of $f$ is at most
its influence up to a universal constant factor. While the FEI conjecture has
been proved for many classes of Boolean functions, it is still not known
whether it holds for the class of Linear Threshold Functions. A natural
question is: Does the FEI conjecture hold for a `random' linear threshold
function? In this paper, we answer this question in the affirmative. We
consider two natural distributions on the weights defining a linear threshold
function, namely uniform distribution on $[-1,1]$ and Normal distribution.
