The logistic distribution is associated with the distributionfunction F(x) = (1+
ID: 2951145 • Letter: T
Question
The logistic distribution is associated with the distributionfunction F(x) = (1+e^(-x))^(-1), - < x < Find the p.d.f. of the logistic distribution and show that itsgraph is symmetric about x=0 Note: The graph is NOT neccessary if it is alot of trouble Thanks for your help The logistic distribution is associated with the distributionfunction F(x) = (1+e^(-x))^(-1), - < x < Find the p.d.f. of the logistic distribution and show that itsgraph is symmetric about x=0 Note: The graph is NOT neccessary if it is alot of trouble Thanks for your helpExplanation / Answer
f(x) = F'(x) = -1/(1 + e-x)2 *-e-x = e-x / (1 +e-x)2 Symmetric about x = 0 --> f(-x) = f(x). Let's demonstratethis. f(-x) = e-(-x) / (1 + e-(-x))2 =ex / (1 + ex)2 = ex /(1 + 2ex + e2x) Multiplying the numerator and denominator by e-2x... f(-x) = [e-2x ex] / [(1 + 2ex +e2x) e-2x] = e-x /(e-2x + 2e-x + 1) = e-x / (1 +e-x)2 = f(x) Thus, f(x) = f(-x).
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