This discussion focuses on calculating the expected value (E(X)) and variance (Var(X)) of a continuous random variable X, given the survival function P(X>x) = e^{-ax} for x ≤ 0, where a is a positive constant. The probability density function is derived as p(x) = -a e^{-ax}. The expected value is computed using the integral E(X) = -a ∫_x^0 x e^{-ax} dx, while the variance is calculated with Var(X) = -a ∫_x^0 (x - E(X))^2 e^{-ax} dx, which simplifies to -aE(X) ∫_x^0 x^2 e^{-ax} - E^2(X).
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