Probability density function

Hi, I have this question that I've been struggling with.

Given is a random distance with probability density function and expected value , then the sampled distance distribution has probability density function , where

Find the form of the distance probability density function and its expected value if the sample distances are fitted by the probability distance function and .

Anyone help will be appreciated. thanks.

I have tried equating the two g(x) but I keep getting something ridiculous like showing