4. Central Limit Theorem

If we add all the samples as N goes to infinity it tends to a gaussian distribution.

What about Cauchy distribution?

Will this theorem hold if we apply the Cauchy distribution?

If this does not work, then what is the interpretation and what is the reason it does not work?

An asymptotically Gaussian variable with a variance that tends to zero as N gets large.

What does it do and what is the physical relevance in engineering?

5. Gaussian Process and Brownian motion

What is the relation between these two?

What is the difference between the gaussian variable and the gaussian process?

Calculate the expected values?

Correlation/joint distribution/marginal distribution/independence

Interdependencies between these concepts

6. Bayes Theorem: Monty's Dilemma

What is the best strategy to win the prize?

Is there another method to solve this without Bayes theorem?