There are two major difficulties that could create problems in the use
of the binomial probability formula: lack of independence and p varying
from trial to trial. Possibly the breakdown of the independence assumption
is the most serious. As an extreme case, say that the outcomes of the
second and subsequent trials would be exactly the same as the outcome
on the first trial; thus each trial would have probability p of success but
they would be totally dependent (as might be in the case of flight
insurance on n executives in one company when they always fly to
meetings together). Here the p.d.f. of X is