The Census Bureau reports that 27% of California residents are foreign-born. Suppose that you choose three Californians at random, so that each has probability 0.27 of being foreign-born and the three are independent of each other. Let the random variable W be the number of foreign-born people you choose.
What are the possible values of W?
Look at your three people in order. There are eight possible arrangements of foreign (F) and domestic (D) birth. For example, FFD means that the first two are foreign-born and the third is not. All eight arrangements are equally likely. What is the probability of each possible outcome?
What is the value of W for each arrangement in (b)? What is the probability of each possible value of W?
What is the mean and standard deviation of the probability distribution of W?
Let U be the number of domestic-born people in the sample minus the number of foreign-born people in the sample; i.e., U = 3 − 2W. What is the mean and standard deviation of U?