A distribution that has been used to model tolerance levels in bioassays is the logisticdistribution with parameters a and ß. The cumulative distribution function of the logisticdistribution isF(x) = [1+e--a)/The parameter a may be any real number; the parameter B may be any positive number. LetX be a random variable with this distribution.Find the probability density function fx(x).a.Show that fx(x) is symmetric around a, that is, fy(« – x) = f;(a +x) forall x.b.Explain why the symmetry described in part (b) shows that µx = a. You may assumeC.that µy exists.

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Asked Feb 21, 2020
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A distribution that has been used to model tolerance levels in bioassays is the logistic
distribution with parameters a and ß. The cumulative distribution function of the logistic
distribution is
F(x) = [1+e--a)/
The parameter a may be any real number; the parameter B may be any positive number. Let
X be a random variable with this distribution.
Find the probability density function fx(x).
a.
Show that fx(x) is symmetric around a, that is, fy(« – x) = f;(a +x) forall x.
b.
Explain why the symmetry described in part (b) shows that µx = a. You may assume
C.
that µy exists.
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A distribution that has been used to model tolerance levels in bioassays is the logistic distribution with parameters a and ß. The cumulative distribution function of the logistic distribution is F(x) = [1+e--a)/ The parameter a may be any real number; the parameter B may be any positive number. Let X be a random variable with this distribution. Find the probability density function fx(x). a. Show that fx(x) is symmetric around a, that is, fy(« – x) = f;(a +x) forall x. b. Explain why the symmetry described in part (b) shows that µx = a. You may assume C. that µy exists.

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