A certain country has 4 regions: North, Eash, South, West. The regions have populations of 3 million, 4 million, 5 milli

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A certain country has 4 regions: North, Eash, South, West. The
regions have populations
of 3 million, 4 million, 5 million, and 8 million, respectively.
Also, the regions has 4 cities, 3
cities, 2 cities and 1 city in them, respectively. Each person in
the country lives in exactly
one of these cities.
(a) Find the average population of a city in this country (this is
called the arithmetic mean
and represents the expected population of a city chosen uniformly
at random from the entire
country).
(b) Show that, without more information, we cannot find the
variance of the population of
a city chosen uniformly at random from the entire country. You can
simply describe what
information we lack in order to compute this.
(c) Suppose you choose a region at random, then choose a city from
that region at random.
Find the expected population of that city.
Hint: Start by finding the PMF of the population size of the
city.