  The problem of finding an explicit formula for the probability density
function of two zero mean correlated normal random variables dates back to
1936. Perhaps surprisingly, this problem was not resolved until 2016. This is
all the more surprising given that a very simple proof is available, which is
the subject of this note; we identify the product of two zero mean correlated
normal random variables as a variance-gamma random variable, from which an
explicit formula for probability density function is immediate.
