  In this note we study the random entire functions defined as power series
$f(z) = \sum_{n=0}^\infty \frac{X_n}{n!} z^n$ with independent and identically
distributed coefficients $(X_n)$ and show that, under very weak assumptions,
they are frequently hypercyclic for the differentiation operator $D: H(\C) \to
H(\C)$, $f \mapsto Df = f'$. This gives a very simple probabilistic
construction of $D$-frequently hypercyclic functions in $H(\C)$. Moreover we
show that, under more restrictive assumptions on the distribution of the
$(X_n)$, these random entire functions have a growth rate that differs from the
slowest growth rate possible for $D$-frequently hypercyclic entire functions at
most by a factor of a power of a logarithm.
