How does variance affect our results?

You mentioned that "for most functions, this will work". What is a function where it does not work?

What will be the cost of solving this equation? Will this be constant time?

Given a random function, is there any proper way to determine the sample importance conveniently?

So we pick points uniformly?

Won't we need to sample more points if the number of dimensions increases, to get the required approximation error? We did discuss it briefly in the last lecture, but I still find this non-intuitive?

How do we compute $|\Omega|$? Isn't the number of points infinite.

What is the variance here and what factors could affect its value?

Why is variance related to this

What is the worst-case running time of calculating the integral?

How and why do we need to consider variance relative to ray-tracing/rendering?

I notice there is also an algorithm Las Vegas Algorithm which aims to find the best match, whereas Monte-Carlo is to find the one to approximate the best match. What would the rendering be like if we implement the Las Vegas one?

will seeds selection affect the image quality?

How does variance affect the final calculation?