Question

In 1991, 72% of children in the United States were living with both parents, 22% were living with mother only, 3% were living with father only, and 3% were not living with either parent (World Almanac and Book of Facts, 1993, p. 945). What is the expected value for the number of parents a randomly selected child was living with? Does the concept of expected value have a meaningful interpretation for this example? Explain.

Answer 1

A child can either live with both his parents, or with only one parent, or with none of his parents.

So there are three outcomes, i.e. 0, 1, 2.

Now, P(0)=0.03

P(1)=0.03+0.22=0.25

P(2)=0.72

Therefore,

Thus, expected value for the number of parents a randomly selected child was living with is 1.69

The concept of expected value does not give us a very meaningful answer in this case. This is because, the number of parents can never be a fractional quantity. It should have been either 0 or 1 or 2. However in this case it is 1.69