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\textbf{Question:}$ Consider a standard Brownian motion (BM), $\{ B(t), t \geq0\}$. What is the distribution of $B(s)+B(t), 0 \leq s \leq t?$ \\\textbf{Solution:} Write $B(s)+B(t) = 2B(s) + B(t) - B(s)$. Then by independent increments of BM, $B(s)$ and $B(t) - B(s)$ are independent. Now, we look...

Hey guys, my friends (and not myself) are doing an assignment to see how online technologies are utilised and how they impact our studies. It would be great if some people can fill out their short survey! They have 60 out of 70 completed ones; nearly their goal. Link...

I understand the proof except for one part of the forward implication (only if) (https://en.wikipedia.org/wiki/Sufficient_statistic#Another_proof). Specifically, $Since $T$ is a function of $X$, we have $f_{\theta}(x,t) = f_{\theta}(x)$ (only when $t = T(x)$ and zero otherwise) I tried...

\noindent $Suppose that $X \sim U_{[0,1]}$ and $Y|(X = x) \sim U_{[0,x]}.$ The probability density function (PDF) of $Y$ can be found by conditioning on $X, \\ \mathbb{P}(Y = y) = \int_y^1 \mathbb{P}(Y = y|X = x)\mathbb{P}(X = x)dx. \\ $I understand how to identify the integral bounds. The...

Only resources we have are assignments and tutorials. Help! D: Like, I've done all the questions. Just looking for more questions to assess my mastery of linear models.

Second year adv math UNSW considering transferring into adv math/econ dual degree because employment. Well, I'm doing linear models and enjoying that, so maybe getting understanding in econometrics would be great. Should I transfer or learn econometrics alone? and also I'll learn to code. Do...