Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 11 (e)
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Question 11 (e)
is an example of a Gamma distribution, a function that may be used to describe certain probabilities.
(e) Draw a large graph of below, incorporating all of the features determined in the previous parts of this question.
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Noting that the domain of is given by , draw its graph based on the information in part (a)-(d).
You can split the domain into three parts, , , and , and draw each piece of the graph.
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Note that the domain of is given as .
Part (a) tells us that the graph of passes through .
From part (b), we get the horizontal asymptote of as . In other words, as goes to infinity, the graph approaches to , i.e., -axis.
From part (c) and (d), we see that is increasing on and decreasing on , while it is concave down on and concave up on .
Collecting the information, we can draw the graph of as follows.