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Just a tip for log-likelihood stuff: after taking the log of the likelihood, continue to simplify the result using log laws such that fractions are eliminated. It'll make differentiation much easier.

I can't make sense out of the question. Is it meant to be (RTP): P( (f(X) - f(Y))(g(X) - g(Y))\geq 0) = 1

Yes!

Re: Statistics LOL! Wikipedia article on '1.96'.

Re: Statistics Are you familiar with indicator functions?

y = cos^-1x => x = cos(y) ... (*) So, (sin(y))^2 + (cos(y))^2 = 1 means sin(y) = sqrt(1 - x^2) Now, differentiate (*) with respect to y, dx/dy = -sin(y) => dy/dx = -1/sin(y) = -1/sqrt(1 - x^2) There are some missing details on plus/minus, but this is the gist of it.

Re: Statistics @Flop21, do you understand why we integrate the PDF of X from x = 1/3 to x = 1?

Thanks for giving me a new perspective on Brownian motion. :)

\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...

Note that -3x + 5 > 0, which means x < 5/3. Now exchange x and y, x = √(-3y + 5), y < 5/3 x^2 = -3y + 5, y < 5/3 y = (5 - x^2)/3, y < 5/3 Therefore, f^{-1}(x) = (5 - x^2)/3, and f^{-1}(x) < 5/3.

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...

The deadline was stated clearly. Why should the lecturer let this slide? Those who hand in late should get punished for not being able to follow instructions or plan ahead. It technically introduces unfairness in terms of completion time for this assignment.

What is sin2x + cos2x equal to?

Re: maths questions help Worked solutions.

Re: maths questions help In my experience, it's either a lack of knowledge in a topic or it requires a whole new perspective on a concept. Assume that I've understood the question and have enough knowledge in the relevant topics. Then I usually employ a systematic approach described by George...

Re: maths questions help No, I apologize for coming off like that, I didn't mean to, but I'm just telling you what I think straight up.

Re: maths questions help If you don't know how to do a question, then consider the event that you don't understand question; you know what to do in this case. Otherwise, you need to figure out, precisely, why you can't do a question. So, if this habit is left unchecked, then you may become...

Here is another way to think about it. Let y = 32x − 1. You cannot differentiate this easily; the problem is the power. To solve this problem, you take logs on both sides to 'bring down' the power: log(y) = (2x - 1)log(3). Make y the subject: y = e(2x - 1)log(3) and differentiate normally...

Re: University Statistics Discussion Marathon I have corrected my original working. Thanks for the checks, I knew something was strange. Below is an easier-to-read version. ___________________________________________________________________________ Given that p = 0.5 = 1-p, P(X \geq 43) =...

Bachelor of Science and take relevant mathematics/actuarial units.