In addition to a small amount of number crunching this probl

In addition to a small amount of number crunching, this problem also asks you to make sure you can keep track of identifiers such as ‘X’, ‘F’, or ‘D’ as specified in the problem. In other words, you must make sure that you are clear about what each of these variables represents. 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 ‘X’ represent the number of foreign-born people in your sample of three people. a) What are the possible values of X? (I.e. What is the sample space of X?) b) Look at your three people in order. There are 8 possible arrangements of foreign (F) and domestic (D) birth. For example, FFD means the first two are foreign born and the third is not. What is the probability of each of the 8 arrangements? c) Think about what we mean when we say ‘X’. Then provide the value of X for each arrangement in question ‘b’. Then calculate the probability of each possible value of X. d) A paragraph above states: “Suppose that you choose three Californians at random…”. If we take 3 Californians, shouldn’t this make the values non-independent of each other since each time we examine one Californian, the populations of all Californians is slightly reduced? If that is the case, why have I said that it is okay to treat these three as independent of each other?

Solution

a)

X= 0,1, 2, 3

b)

8 C 3 = 56

c)

x=0---1/56

x=1---8/56

x=2---28/56

x=3---19/56

d)

I can gladly help you but you should post it in a new question