## 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#