Thursday, July 30, 2009

Probability .?

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 chose.





(a) what are the possible values of W?





(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-born and the third is not. What is the probability of each arrangement?





(c) What is the value of W for each arrangemen in (b)? What is the probability of each possible balue of W? (this is the distribution of a Yes/no response for an SRS of size 3. In principle the same idea work for an SRS of any size.)

Probability .?
(a)The possible values of W are





0, 1, 2, and 3





(b) since there are eight possible arrangements, the probability of each arrangement is 1/8, or 12.5%





(c) The value of W for each arrangement is





0, 1, 1, 1, 2, 2, 2, 3





The probability of each possible value is





0= 1/8 or 12/5%


1= 3/8 or 37.5%


2= 3/8 or 37.5%


3= 1/8 or 12/5%


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