ake the derivative of f(x) = lae-lxxa-1 with respect to x and set the derivative equal to 0.  This is a real question arising in finding the mode of the gamma distribution, i.e., what x makes the probability density greatest.  The letters l and a stand for positive constants, and x is a non-negative real number. Show that if a < 1, the solution is impossible.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...
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Take the derivative of f(x) = lae-lxxa-1 with respect to x and set the derivative equal to 0.  This is a real question arising in finding the mode of the gamma distribution, i.e., what x makes the probability density greatest.  The letters l and a stand for positive constants, and x is a non-negative real number. Show that if a < 1, the solution is impossible.

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