# Expected value of $1/X$.

Given a random variable $X$ with probability density function $$f(x)=\frac5{x^6}\mathbf 1_{\{x>1\}}$$ I am trying to find the mean of $1/X$. After making the transformation I find that $f(1/x)=5x^4$. So far I've come up with only whole numbers but the answer is supposed to be a fraction.

Any ideas?

• You mean that $f(x)=5/x^6$ is the pdf? – Jimmy R. Feb 21 '16 at 10:12
• Your transformation is fine, but what happened to the indicator function? – Will Orrick Feb 21 '16 at 10:29

$$<1/x>=\int_1^\infty dx (1/x)5/x^6=5\int_1^\infty dx\frac{1}{x^7}=\frac{5}{6}\ .$$