An article in American Heart Journal ["Long-term survival after successful in-hospital cardiac arrest resuscitation" (2007, Vol 153(5),pp. 832-836)] examined long-term survival of patients after in-hospital cardiac arrest. In this study, outcomes of 732 patients over 10years were analyzed. Suppose that the probability density function of patient mortality after in-hospital cardiac arrest (in years)follows f(x) = 0.5e-0.5(x-3) for x > 3.Let a continuous random variable X denote patient mortality after in-hospital cardiac arrest (in years).(a) What are the mean and the variance of X?E(X)=V (X) =i(b) Determine the probability that X is more than eight years.Round your answer to three decimal places (e.g. 0.987).P(X> 8) =

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College Algebra

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(a) What are the mean and the variance of X? E(X) = 1 V(X) = i (b) Determine the probability that X is more than eight years. Round your answer to three decimal places (e.g. 0.987). P(X> 8) =