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1) We've collected data on the percentage of the population of each county in California that is considered obese, using clinical measures, and that has been diagnosed with diabetes. We have constructed two random variables, Obesity and Diabetes, of the following forms (note: how the categories are constructed is irrelevant),
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a) We shall note that the probability of obesity = 2 may be further divided into 3 subgroups, that is,
P(obesity = 2) = P(obesity = 2 and diabetes = 1) + P(obesity = 2 and diabetes = 2) + P(obesity = 2 and diabetes = 3) = 0.00 + 0.278 + 0.122 = 0.4.
Using the same reasoning as above, we complete the table.
Ob = 1 Ob = 2 Ob = 3 F(d)
Diab = 1 0.017 0.00 ...
This solution provides an introductory explanation of how to calculate a probability and the conditional distribution of the given variable.