Recent content by jojay99

Hi guys, What is the limit of (1+f(x))^g(x) as x approaches positive infinity? We were taught two limits in class: lim (1+f(x))^g(x) = lim exp(f(x)*g(x)) and lim (1+f(x))^g(x) = exp(-0.5*C) if lim g(x)*f(x)^2=C We were given a proof of the first one in class so I'm sure...

Hey guys, I have a quick question. Suppose X is a chi squared random variable with n degrees of freedom and Y is another independent chi squared random variable with n degrees of freedom. Is X/Y ~ 1 ? Intuitively, it makes sense to me but I'm not too sure.

I would use either a linear or non-linear mapping of the variables, f: $ \mathbb{R}^{6} \cup \{0,1\} \rightarrow \mathbb{R} $, to give you a score. The mapping is really up to you to decide.

Thank you guys for your help. Yeah, I was referring to point wise convergence of the pdfs. I always thought that Scheffe's Theorem only applied to continuous random variables. I guess I'm wrong.

I thought so. However, using induction to prove that doesn't seem natural (pun intended) to me.

So convergence in the probability density functions implies that the cdfs converges?

Not true. Otherwise, we should all be single cell organisms.

I'm curious. How would you disprove that using induction? They're both countably infinite. The only way I can think of is using bijections between both sets.

Ipau001, I think I understand where you're coming from. Hopefully, my explanation is correct and makes sense. We use induction to show that all elements in a countable set (e.g. the set of natural numbers) have a certain property. So to prove a statement is false, we could use induction to show...

Hey guys, In class, I was shown that the Binomial prob density function converges to the Poisson prob density function. But why does this show that the Binomial distribution converges in distribution to the Poisson dist. ? Convergence in distribution requires that the cumulative density...