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Interestingly, P(B), the unconditional probability that the second part selected is defective, without any knowledge of the rst part, is the same as the probability that the rst part selected is defective. Yet, our goal is to assess independence. Because P1B A2 does not equal P(B), the two events are not independent, as we suspected. When considering three or more events, we can extend the de nition of independence with the following general result.

Entity = Data entity Relationship = Data relationship People = Role Work = Deliverable e.g., System design e.g., Technology architecture e.g., Presentation architecture

Lauren stated that one of the best features of her job is that she gets to choose the days she wishes to work, which gives her the opportunity to enjoy social time with friends and family and ample time to take care of the household Lauren s medical history is relatively unremarkable She is farsighted and, therefore, requires the use of reading glasses During a recent physical examination, her physician found her hearing to be excellent and no medical conditions were noted Lauren has had no major illnesses, injuries, or hospitalizations She does not use nicotine or illegal drugs When asked about her pattern of alcohol use, Lauren stated that she enjoys a glass of wine every night with dinner, but never drinks large quantities at a time She added that her eating habits are a bit erratic and her diet is not balanced enough.

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De nition The events E1, E2, p , En are independent if and only if for any subset of these events Ei1, Ei2, p , Eik , P1Ei1 Ei2 p Eik 2 P1Ei1 2 P1Ei2 2 p P1Eik 2 (2-10)

She also expressed a concern about not getting enough sleep on a daily basis and that to get a really good night of sleep, she has to take an over-the-counter sleep aid such as Sominex, but no other medications were noted Lauren reported no history of learning problems in her family, but she does have a history of psychological disorders in her family Her mother suffered from a severe case of menopausallyrelated depression at the age of 51 She was treated for her disorder and, after fighting the disorder for thirteen years, regained her psychological health However, after a fifteen-year period of remission, her mother s depression recently resurfaced She was admitted to a psychiatric hospital just a few weeks ago Lauren stated that this has been a severe stressor in her life and has dictated her daily activities for the past few weeks.

This de nition is typically used to calculate the probability that several events occur assuming that they are independent and the individual event probabilities are known. The knowledge that the events are independent usually comes from a fundamental understanding of the random experiment. EXAMPLE 2-26 Assume that the probability that a wafer contains a large particle of contamination is 0.01 and that the wafers are independent; that is, the probability that a wafer contains a large particle is

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(S12-2)

She has been unable to teach on a regular basis, as her mother s condition demands the availability of constant care She remarked that she feels lucky to have a very strong support system to help her through this tough time She has a close relationship with her husband and her two daughters, and a good friend who lives next door Luckily, her other siblings live close by and her father lives with her mother, so they have been able to share the responsibilities of her mother s care Lauren stated that she enjoys jogging and working in her garden during her free time Lauren believes her strengths to be that she is skilled in organizing her time and activities and she is a very caring and giving mother to her two daughters Lauren stated rather frankly that her weaknesses are her poor self-image and low self-esteem.

These models can include not only the rst-order relationships, such as Equation S12-2, but polynomial models, and other more complex relationships as well. In fact, we could write the linear regression model as Y

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