statistics proof

1. The problem statement, all variables and given/known data

so i was oping to prove the following are equivalent: [tex]\int_{-\infty}^{\infty}c^m B_x(c)dc=\lim_{n \to \infty}\frac{1}{n}\sum_{i=1}^{n}x_i^m[/tex]





2. Relevant equations

[tex]\int_{-\infty}^{\infty}B_x(c)dc=1[/tex]

[itex]x_i[/itex] is a random variable.

[itex]B_x(c)[/itex] is a pdf



3. The attempt at a solution

i was going to write the first integral as a sum and equate the two summations as: [tex]\lim_{n \to \infty}\sum_{i=1}^{n}\underbrace{\Big(-n+\frac{n-(-n)}{n}\Big)B_x \Big(-n+\frac{n+(-n)}{n}\Big)}_{f(x_i)}\underbrace{\frac{n-(-n)}{n}}_{\Delta x}[/tex] [tex]x_i=a+\frac{b-a}{n}[/tex]but i'm not really sure what to do next. any help is appreciated. also, if i need to provide more info please let me know.



for the record, this is not an assignment but is a problem i found in my text and was curious.



thanks!