Example 6.1.5 from Section 6.1, which illustrates stochastic immigration, was generated by adding two individuals with probability

Question:

Example 6.1.5 from Section 6.1, which illustrates stochastic immigration, was generated by adding two individuals with probability 0.5 and zero individuals with probability 0.5 for 100 generations. The results in the figure show final populations of 106 and 96.
1. How can these results be described in terms of the binomial distribution?
2. What is the expected number after 100 generations?
3. What is the variance after 100 generations?
4. Write the probability of exactly 106 in terms of the binomial distribution.