If the moment-generating function of X is given by M(t) = e^(500t+5000t^2), find P[27,060 ≤ (X - 500)^2 ≤ 50,240].
Added by Michael G.
Step 1
We can do this by finding the first and second derivatives of the moment-generating function M(t) and evaluating them at t = 0. M'(t) = \frac{d}{dt}(e^{500t + 5000t^2}) = (500 + 10000t)e^{500t + 5000t^2} M''(t) = \frac{d^2}{dt^2}(e^{500t + 5000t^2}) = (500 + Show more…
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