How would you show that the expected value of the logistic distribution is equal to it's mean? ie E(X)=mu slightly simplified: Various substitutions I've tried don't seem to work, , etc haven't worked to well for me.
Last edited by evidor; Oct 5th 2008 at 10:03 PM.
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Originally Posted by evidor How would you show that the expected value of the logistic distribution is equal to it's mean? ie E(X)=mu slightly simplified: Various substitutions I've tried don't seem to work, , etc haven't worked to well for me. Since it follows that . Therefore: . Substitute and split the integral up: . The first integral is equal to zero since the integrand is an odd function of w. The second integral is simple to perpetrate and is equal to 2. Then .
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