A distribution that has been used to model tolerance levels in bioassays is the logistic distribution with parameters ? and ?. The cumulative distribution function of the logistic distribution is
The parameter ? may be any real number; the parameter ? may be any positive number. Let X be a random variable with this distribution.
a. Find the probability density function 
.
b. Show that is symmetric around ?, that is, 
for all x.
c. Explain why the symmetry described in part (b) shows that 
= ?. You may assume that exists.
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