6. Ten students are selected at random from this university. The selected students are

independently and identically distributed. Let X denote the number of students out of ten that have no siblings.

a. Find the mean and variance of X. (2 points)

b. What is the probability that X = 2? (2 points)

7. n (n > 10) students are selected at random from this university. The selected students are independently and identically distributed. Let A denote the event that exactly two out of the n students have no siblings. Find the smallest n that makes A unusual. (2 bonus points)

The tables are

# of siblings. Frequency #of siblings Relative frequency

0. 200 0 20%

1 400 1 40%

2 350 2 35%

3 50 3 5%