  It is well known that random bipartite pure states are typically maximally
entangled within an arbitrarily small error. Showing that the marginals of
random bipartite pure states are typically extremely close to the maximally
mixed state, is a way to prove the above. However, a more direct way to prove
the above is to estimate the distance of random bipartite pure states from the
set of maximally entangled states. Here, we find the average distance between a
random bipartite pure state and the set of maximally entanglement states as
quantified by three different quantifiers of the distance and investigate the
typical properties of the same. We then consider random pure states of a single
quantum system and give an account of the typicality of the average $l_1$ norm
of coherence for these states scaled by the maximum value of the $l_1$ norm of
coherence. We also calculate the variance of the $l_1$ norm of coherence of
random pure states to elaborate more on the typical nature of the scaled
average $l_1$ norm of coherence. Moreover, We compute the distance of a random
pure state from the set of maximally coherent states and obtain the average
distance.
