12.32Foreign-born Californians. The CensusBureau reports that 27% of California

Question

12.32Foreign-born Californians. The CensusBureau reports that 27% of California residents are foreign-born.Suppose that you choose three Californians at random, so that eachhas probability 0.27 of beingforeign-born and the three choices are independent of each other.Let the random variable Xbe the number of foreign-born people you chose.

(a) What are the possible values ofX?

(b) Look at your three people in order.There are eight possible arrangements of foreign (F) and domestic(D) birth. For example, FFD means the first two are foreign-bornand the third is not. Write down all eight arrangements and findthe probability of eacharrangement.

(c) What is the value of X foreach arrangement in (b)? What is the probability of each possiblevalue of X? (You have found the distribution of a Yes/Noresponse for an SRS of size 3. Inprinciple, the same idea works for an SRS of any size.)

Explanation / Answer

(a) 0, 1, 2, 3 (ranging from none to all foreign born). (b) FFF, FFD, FDF, FDD, DFF, DFD, DDF, DDD. (c) FFF (X = 3), FFD (X = 2), FDF (X = 2), FDD (X = 1), DFF (X =2), DFD (X = 1), DDF (X = 1), DDD (X = 0). You get the values of X by just counting the number of Fs in thesequency. 1 out of 8 possibilities has X = 3. Pr(X=3) = 1 3 out of 8 possibilities has X = 2. Pr(X=2) = 3 3 out of 8 possibilities has X = 1. Pr(X=1) = 3 1 out of 8 possibilities has X = 0. Pr(X=0) = 1

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