Answers
Assuming we let
Explanation:
The pdf
The method of moments tells us to equate theoretical moments to their corresponding sample moments (about the origin), and then solve for the parameter.
For this question, we begin by setting the first theoretical moment
#E[X]=theta=1/nsum_(i=1)^nX_i=M_1#
or simply
#color(white)(E[X]=)theta=1/nsum_(i=1)^nX_i#
Since there is only one parameter to estimate, we do not need to use any 2nd moments, etc.
The equation above gets solved for
Looks like the equation is already sovled for
#hattheta_(MM)=1/nsum_(i=1)^nX_i#
#color(white)(hattheta_(MM))=barX#
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