Search results

I get 90 seconds.

What you are calculating is the probability that X ≤ alpha, but we need the probability that the proportion is less than or equal to alpha (whereas X is the number). $\noindent So you'd need to find the probability that $X \leq \alpha n$. So sum the pmf from $k = 0$ to $N\left(\alpha\right)$...

$\noindent In general, say we're given a plane equation in $\mathbb{R}^{3}$: $\Pi: \bold{x} = \bold{a} + \eta \bold{v}_1 + \xi \bold{v}_2$ (parametric vector equation). Then a normal to the plane is $\bold{n} := \bold{v}_1\times \bold{v}_2$ (in other words, cross the two direction vectors and...

Well it's basically a coincidence it happened to the point they give in the line's parametric equation (because they could have used a whole host of other points for the exact same line's equation (i.e. any other point on that line)). The cross product would be used to find a normal to the...

The Bernoulli distribution is the binomial distribution with n = 1. In fact, a Bin(n,p) random variable is just a sum of n i.i.d. (independent and identically distributed) Bern(p) (Bernoulli with parameter p) random variables. The geometric distribution can be considered a special case of the...

You might want to check out this post (and the thread in general): http://community.boredofstudies.org/238/extracurricular-topics/342550/announcement-bostes-significant-change-calculus-courses.html#post7033123 . From memory, some changes include that conics is being removed from HSC MX2, with...

$\noindent It will be easier to use the formula $\mathrm{Var}\left[X\right] = \mathbb{E}\left[X^2\right] - \mu^2$ here. Note that the pmf for the discrete uniform r.v. $X$ is $p_k = \frac{1}{n}$ for $k=1,2,\ldots n$ (and 0 otherwise), as you stated. Now, recall the formula $\sum _{k=1}^{n} k^2 =...

The method you used isn't too long, and will lead to the right answer if done correctly. You'll basically end up with the plane equation of the form ax + by + cz = d . Then sub. in the line coordinates to this and solve for lambda (which is easy to solve for since it's just a linear equation in...

To sketch y = f(4x), take the graph of y = f(x) and compress it horizontally by a factor of 4. So if you have a graph of y = 3.cos(x), then squeeze this horizontally by a factor of 4. So before the positive zeros were at pi/2, 3pi/2, 5pi/2, 7pi/2, … . Now, they'll be at one-quarter of each...

$\noindent You need to type them in between tex tags.$ Type [tex.] [/tex.] (without the full stops). Then place your codes inside those. Also, it's good to leave spaces between things, like put a space between \leq and 5 for example, otherwise the code can mess up here sometimes.

He may be very, very annoyed.

Yeah, you can use both \ge and \geq (similarly \le vs. \leq and \ne vs. \neq). You can read about this here: http://tex.stackexchange.com/questions/49452/is-there-a-difference-between-ge-and-geq-or-equivalentely-between-le-and-leq .

Use \geq for ≥, \leq for ≤, and you can just use > and < for strict inequalities. (If you want slanted equality line in the non-strict inequalities, it is \geqslant or \leqslant.)

I said he does mind his own business – I didn't say though that's the only thing he does. (Plus, most of the things he said were in jest.)

I'm guessing he does mind his own business.

Why do you want to see him fail?

Rectilinear motion is motion along a straight line, so only one-dimensional motion. For projectile motion in the HSC, it's two-dimensional. (Referring to spatial dimensions.) Further info and equations about rectilinear motion may be found here: https://en.wikipedia.org/wiki/Linear_motion ...

The word syllabi is also used.

Re: HSC Chemistry Marathon 2016 $\noindent Let the $\text{K}_{\text{a}}$ be $K$. We know that $K = 10^{-\text{pK}_{\text{a}}} = 10^{-4.76}$.$ $\noindent Writing out the formula for $K$, we have $K=\frac{\left[\text{A}^{-}\right]\left[\text{H}^{+}\right]}{\left[\text{HA}\right]}$. Now, both...

Re: HSC Chemistry Marathon 2016 Ka is the acid dissociation constant for an acid. pKa is the colog (negative log-base-10) of that (by definition of "p"). Ka is a quantitative measure of the strength of an acid in solution. It's not in the HSC Chemistry syllabus (unfortunately!) though – it...