PROBLEM 7: SAMPLING FAMILIES (3 points possible)

Question

We are given the following statistics about the number of children in the families of a small village.

There are 100 families: 10 families have no children, 40 families have 1 child each, 30 families have 2 children each, 10 families have 3 each, and 10 families have 4 each.

If you pick a family at random (each family in the village being equally likely to be picked), what is the expected number of children in that family?

- unanswered
If you pick a child at random (each child in the village being equally likely to be picked), what is the expected number of children in that child's family (including the picked child)?

- unanswered
Generalize your approach from part 2: Suppose that a fraction pk of the families have k children each. Let K be the number of children in a randomly selected family, and let a=E[K] and b=E[K2]. Let W be the number of children in a randomly chosen child's family. Express E[W] in terms of a and b using standard notation.

E[W]=- unanswered

Answer 1

17/10

41/17

b/a