The following table gives the joint probability of X and Y, where X represents a

Question

The following table gives the joint probability of X and Y, where X represents a person’s poverty status (below or above the poverty line as defined by the U.S. government), and Yrepresents the person’s race (white, blacks only, and all Hispanic).

a. Compute f(X|Y=white); f(X|Y =black), f(X|Y=Hispanic), and f(X|Y=Asian), where X represents below the poverty line.

b. What general conclusions can you draw from these computations?

c. Are race and poverty status independent variables? How do you know?

Explanation / Answer

a) P(X=below poverty line | Y = white) = 0.054/(0.054+0.615)

= 0.0807

b) P(X=below poverty line | Y = black) = 0.0315/(0.0315+0.097)

= 0.2451

c) P(X=below poverty line | Y = hispanic) = 0.0343/(0.0343+0.123)

= 0.2181

d) P(X=below poverty line | Y = Asian) = 0.0046/(0.0046+0.0406)

= 0.1018

b) Whites and Asians are the races with lesser proportion of people belonging to lower than poverty line, where black and hispanic races have higher proportion below poverty line. With almost one-fourth of the population below poverty line, blacks are having maximum proportion below poerty line.

c) No, if the race and poverty status were independent, all probabilities in part (a) of the question would have been the same. So,race and poverty status are not independent.

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