4. Let X be a lifetime (in hours) of a lightbulb and suppose that X has a PDF of e0.001x f(x) = if x 2 0. %3D 1000 if x < 0 (a) Determine P(X < 1000) (b) Determine P(100 < X < 1000) (c) Determine a number x such that a lightbulb survives the age x with probability of 0.7. (d) Determine the expected value (e) Determine its variance and standard deviation

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