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 F(x) 1 e(x) 1 The parameter may be any real number the parameter may be any positive number Let X be a rando...

A distribution that has been used to model tolerance levels in bioassays is the logistic distribution with

Question:

A that has been used to model tolerance levels in bioassays is the logistic with parameters α and β. The cumulative function of the logistic is
F(x) = [1 + e−(x−α)/β ]−1
The parameter α may be any real number; the parameter β may be any positive number. Let X be a random variable with this Find the probability density function fX (x).
b. Show that fX (x) is symmetric around α, that is, fX(α − x) = fX(α + x) for all x.
c. Explain why the symmetry described in part (b) shows that μX = α. You may assume that μX exists.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...