Question: Family size. The Census Bureau gives this distribution for the number of people in American families in 2006:
Family size 2 3 4 5 6 7
Proportion 0.45 0.23 0.19 0.09 0.03 0.02
(a) This is also the probability distribution (ignoring roundoff errors that make these proportions add to 1.01) for the size of a randomly chosen family. The expected value of this distribution is the average number of people in a family. What is this expected value?
(b) Suppose you take a random sample of 1000 American families. How many of these families will be of size 2? Sizes 3 to 7?
(c) Based on your calculations in part (b), how many people are represented in your sample of 1000 families?
(d) Calculate the probability distribution for the family size lived in by individual people. Describe the shape of this distribution. What does this shape tell you about family structure?