Researchers are studying a group of 20 people who have recently joined a friendship-matchmaking app. Each pair of people among this 20 will connect and become friends with probability
0.2
, independently of other pairs. (a) Let
X i
​
be the random variable denoting the number of friends from this group that person
i
makes on the app. What familiar distribution and parameters describes
X i
​
? (b) What is the expectation and variance of
X i
​
? (c) What is the expected number of people who will end up with at least 3 friends from the group on the app? (d) Let
Y
denote the total number of friendships formed within this group on the app. Compute Ex[Y] and
Var[Y]
, making sure not to double-count friendships (a friendship between
i
and
j
adds
I
to the total).