The various distributions in the reading this week and last week entail probabil
ID: 3047856 • Letter: T
Question
The various distributions in the reading this week and last week entail probability curves that mathematically differ according to a group of parameters. Different parameters allow for specification of the shape, scale, and location of the distribution.
Discuss the role that these parameters play in establishing the characteristic form for each distribution. Consider why our text doesn’t discuss the location parameter very much. Why might that be? Also, if we strip away these parameters from the various distribution formulas, what’s typically left? Treat this thread as a conceptual exploration, not a detailed mathematical proof.
The various distributions in the reading this week and last week entail probability curves that mathematically differ according to a group of parameters. Different parameters allow for specification of the shape, scale, and location of the distribution.
Discuss the role that these parameters play in establishing the characteristic form for each distribution. Consider why our text doesn’t discuss the location parameter very much. Why might that be? Also, if we strip away these parameters from the various distribution formulas, what’s typically left? Treat this thread as a conceptual exploration, not a detailed mathematical proof.
Explanation / Answer
(a) Why our text doesn't discuss the location parameter very much:
The location parameter tells us where our graph is located i.e., where on the horizontal axis the graph is centered.The effect of the location parameter is to translate the graph on either side. It simply shifts the graph left or right on the horizontal axis, without making any alteration in the shape of the curve. Since in general we are only interested in the shape of the curve, our text doesn't discuss the location parameter very much.
(b) If we strip away these parameters from the various distribution formuas, typically nothing is left.
EXPLANATION: The three parameters: shape, scale and location together completely determine the curve: Shape parameter determines the shape of the curve: by changing the shape parameter, we can get any shape of the curve.
The scale parameter does not change the shape, but stretches or shrinks the curve.
Thus, if we remove all the 3 parameters, we are left with nothing.
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