(Solved): 6. [15 pts] Show that if f is a PDF and the integral x2f(x)dx exists, then the integ ...

6. [15 pts] Show that if $f$ is a PDF and the integral ${\int }_{-\infty }^{\infty }{x}^{2}f(x)dx$ exists, then the integral ${\int }_{-\infty }^{\infty }|x|f(x)dx$ exists. (This is from question number 14 on page 280 of the book which includes a helpful hint.) Why is this result important? (Why would we care about the existence of the second integral?)