punuuiht ii ie sense of Definition 44 then event B is indepe

punuuiht ii ie sense of Definition 4.4, then event B is independent of event A in the sense of Definition 4.3. 44 The U.S. National Center for Health Statistics compiles data on injuries and publishes he information in Vital and Health Statistics. A contingency table for injuries in the United tates, by circumstance and sex, is as follows. Frequencies are in millions. Circumstance Work Home Other Total Male 8.0 Si 8.0 9.8 17.8 35.6 Female 13 11.6 129 25.8 S2 Total 9.3214 30.7 61.4 a) Are events Ci and S2 independent? Explain. b) Is the event that an injured person is male independent of the event that an injured person was hurt at home? Explain. 4.45 Refer to the joint probability distribution in Exercise 4.8 on page 135 for living arrange ment and age of U.S. citizens 15 years of age and older. Are events A2 and Li independent? Interpret your answer f Yahtee five halanced dice are rolled. What is the probability

Solution

a) For checking C1 and S2 are independent we see whether

P(C1S2)=P(C1)P(S2)

Left side = 1.3/61.4 = 0.0211

Right side = 9.3(25.8)/61.4^2 = 0.0636

AS the two are not equal, we conclude that C1 and S2 are not indepdent.

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Injured person is a male - C1

Injured person at home -S2

C1 and S2 are not independent as per part a