Need some help understanding the concept of the Weak Law of Large Numbers and the Continuous Mapping theorem. Attached is a screenshot of one of my problem sets. I've been stuck on this for a while.

If you could provide an explanation for b. and c. that would be great!

Cine neat feature of the geometric mean is that although it is dened in terms of productsI we can use properties of logarithms to rewrite these products in terms of sums. Why might this be useful? Well? it makes the math easier! Here, for the uniform where all values are positiveI you can 1write the geometric mean as Are you able to see why this statement holds? If not, talk about it with your study group. b. [3 points} Apply the WLLN to compute the probability limit of the term that within the exponent. That is? compute . 1 \" 22: n 2\"\" e Hint 1: Because you are working with a uniform distribution, whet expression does % 23:1 remind you of? o Hint 2: You can use an integral solver to compute the value of I; loader. c. [3 points) Apply the Continuous Mapping Theorem to nd the probability limit plim G\". nboo