Here is my question and here is my partial solution.
I am uncertain if I proved the hint correctly, and I am basically stuck now after proving the hint. I have seen a solution to a similar question on Math Stack Exchange, but there are some differences that I don't think I can use the same steps. Furthermore, another solution I have come across is using the Basic Inequality, which was never covered in my class.
If my proof is wrong for the hint, then please correct it for me. Furthermore, it will also be great if you can provide some solutions or hints to answer the question completely. I was thinking of using the Chebyshev's or Markov's inequalities (including their variants), but I can't seem to conclude the answer.