2. (40 points) Is there a relationship between smoking tobacco products and cancer? The following table reports the results of a national study of 137,243 American men. Each male in the study was classified according to his cigarette-smoking status and whether or not he died from tobacco-related cancer. Contingency Table Died from Cancer (D) | Did not Die from Cancer (D') Totals Never Smoked Cigarettes (N) | 782 120,747 121,529 Former Cigarette Smoker (F) 91 7,757 7,848 Current Cigarette Smoker (S) 141 7,725 7,866 Totals 1,014 136,229 137,243 Joint Probability Distribution Table Died from Cancer (D) Did not Die from Cancer (D') Totals Never Smoked Cigarettes (N) |0.0057 0.8798 0.8855 Former Cigarette Smoker (F) 0.0007 0.0565 0.0572 Current Cigarette Smoker (S) 0.0010 0.0563 0.0573 Totals 0.0074 0.9926 1.0000 a. What is the probability that a man selected at random never smoked and died of cancer? b. Given that a man is a former smoker, what is the probability that he died of cancer? c. Given that a man never smoked, what is the probability that he died of cancer. d. Are smoking and cancer independent events? Provide statistical proof