I have already asked this question on stack but for some strange reason I didn't get enough help/ people didn't respond back so I am asking this again.  A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?  I am really confused by this problem. My first initial thought was to do:  $$\frac{{7 \choose 5} {5 \choose 2}}{ {12 \choose 7}}$$  I was given a recommendation to account for the last 2 question that weren't answered. I am not 100% sure about this.
A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?  I am really confused by this problem. My first initial thought was to do:  (5 chose 7)(7 chose 0)/ (12 chose 7)  I am not 100% sure about this though.
Normality test with large data set I think I am dealing with this issue   I have large data set(10k data points) that slightly diverges from normal, and I get p-value of 0. I am interested in having perhaps a more crude test that tells me if data is extremely divergent from normal, versus looking somewhat normally distributed. I am currently trying Kolmogorov-Smirnoff, and in both cases I just get p-value of 0. Any alternatives?  I also looked at this:   So, taking all this into consideration, is there any kind of test I can perform that distinguishes between data that's roughly normal, and not normally distributed at all?  I am using scipy. Find the integer solutions: $$a·b^5+3=x^3,a^5·b+3=y^3$$ This is the first problem of today's USAJMO (has finished),I only find a trival result that $x\equiv y \pmod6$ and $abxy≠0 \pmod 3$.  Thanks in advance! "All of the ...." or " All the ... "? How can I test the quality of a RNG? On electronics.stackexchange we had  about constructing a True Random Number Generator. Since the method relies on noise, which isn't deterministic, the only way to test the quality of the RNG seems to be empirical. Not being a statistician I suggested to test a long bit sequence for normality, but I have no idea what outcome is acceptable and what isn't. For instance counting single bits I guess we have a thumbs-up for a 499500/500500 distribution, but when is the ratio too much skewed to be acceptable? Same for 2-bit and longer sequences. Of course, if testing for normality is a Bad Idea™, I'd like to hear it, including better alternatives.    edit Diehard was mentioned a few times, but I'm not sure this answers my question. The normality test should give a normal distribution, with better bell curve approximations for longer sequences. Diehard seems also to have tests which either should result in normal or exponential distributions. But my question remains: how do I judge the results? Just by looking at the curve and discern a bell curve in it? To get back at my first example, a 499500/500500 distribution is definitely OK, and a 950000/50000 distribution definitely is a no-no, so where does the switch-over happen? Using Windows DLL from Linux Infinite Geometric Series Formula Derivation What are the relationship between administrators groups of domain, dev computer and of Sharepoint services? I know-know I can search and read but anyway I would need to ask in order to escape possible typos, personal misunderstandings and to better remember.     I develop on a machine with installed Sharepoint 2010 Sever where I have local groups:     Administrators Description: Administrators have complete and unrestricted access to the computer/domain   WSS_Admin_WPG Description: Members of this group have write access to system resources used by Microsoft SharePoint Foundation      **Does the description of "Administrators" ("computer/domain") imply all privileges of "WSS_Admin_WPG" ?    Does the description of **WSS_Admin_WPG (in part of "system resources used by Microsoft SharePoint Foundation") imply Sharepoint Server?**    The WSS_Admin_WPG group has entries of:     "BUILTIN\Administrators (S-1-5-32-544)" group   and some user domain accounts   Is "BUILTIN\Administrators (S-1-5-32-544)" group the same (alias to?) as "BUILTIN\Administrators" entry I observe among Sharepoint Farm Administrators (through "Central Administration")?       Is the entries of domain accounts excessive (or necessary)     in "WSS_Admin_WPG" if these accounts make part of "Administrators" group?     in "Farm Administrators" if these accounts are part of "BUILTIN\Administrators (S-1-5-32-544)" group?     What are relationship (difference) between "BUILTIN\Administrators" and "Administrators"? systemd in ubuntu 14.04 Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity How to keep processes running after ending ssh session? Let's say I launch a bunch of processes from a ssh session. Is it possible to terminate the ssh session while keeping those processes running on the remote machine? Converting string into datetime EDIT: As of Java 8, static methods are now allowed in interfaces.  Here's the example:  public interface IXMLizable&lt;T&gt; {   static T newInstanceFromXML(Element e);   Element toXMLElement(); }   Of course this won't work.  But why not?  One of the possible issues would be, what happens when you call:  IXMLizable.newInstanceFromXML(e);   In this case, I think it should just call an empty method (i.e. {}).  All subclasses would be forced to implement the static method, so they'd all be fine when calling the static method.  So why isn't this possible?  EDIT: I guess I'm looking for answer that's deeper than "because that's the way Java is".   Is there a particular technological reason why static methods can't be overwritten? That is, why did the designers of Java decide to make instance methods overrideable but not static methods?  EDIT: The problem with my design is I'm trying to use interfaces to enforce a coding convention.  That is, the goal of the interface is twofold:   I want the IXMLizable interface to allow me to convert classes that implement it to XML elements (using polymorphism, works fine). If someone wants to make a new instance of a class that implements the IXMLizable interface, they will always know that there will be a newInstanceFromXML(Element e) static constructor.   Is there any other way to ensure this, other than just putting a comment in the interface? It is a common assumption (and, as far as historical stock market data goes, also proven) that the stock market is always growing if you enlarge the time window long enough . In other words: The stock market always goes up in the long term. Is, therefore, the conclusion valid that you can totally invest as much as you want at any point in time you want and you can never go wrong, if  You diversify strong enough (invest &quot;in the world&quot;) You do not need to urgently sell your assets at any point in time  If yes, all that strategies that rely also on diversified, long-term investments (Dollar-Cost-Averaging &amp; Rebalancing, .. what others do you know?) are just to optimize the yiels, but you'd make profit even without those strategies. Is that correct? Best method for short time-series Prove that if a function's average is nondecreasing then the function is nondecreasing. Let $\omega:\mathbb{R}_+\to\mathbb{R}_+$ such that $\omega(0) = 0$ and $\xi(s) = \frac{1}{s}\int\limits_{0}^s \omega(t)dt$ is nondecreasing, i.e., $\forall s,s': s\leq s'$, $\xi(s)\leq \xi(s')$. Show that $\omega(t)$ is nondecreasing a.e., i.e. find a function $w(t)$ such that $w$ is nondecreasing and $\omega = w$ a.e.  I was able to show the reverse implication easily, that if $\omega$ is nondecreasing then $\xi$ is nondecreasing. This way seems more difficult. How to recover/reset forgotten Gnome Keyring Password? How to find the determinant of this $3 \times 3$ Hankel matrix? Today, at my linear algebra exam, there was this question that I couldn't solve.   Prove that $$\det \begin{bmatrix}  n^{2} &amp; (n+1)^{2} &amp;(n+2)^{2} \\  (n+1)^{2} &amp;(n+2)^{2}  &amp; (n+3)^{2}\\  (n+2)^{2} &amp; (n+3)^{2} &amp; (n+4)^{2} \end{bmatrix} = -8$$   Clearly, calculating the determinant, with the matrix as it is, wasn't the right way. The calculations went on and on. But I couldn't think of any other way to solve it. Is there any way to simplify $A$, so as to calculate the determinant? Is being a Cauchy sequence equivalent to $ \lim_{n\to+\infty}d(x_{n+k},x_n)=0$ for every $k$? Is this statement true?      In a metric spase $(E,d)$, a sequence $(x_n)$ is Cauchy if and only if $  \forall k\in \mathbb{N}, \lim_{n\rightarrow+\infty}d(x_{n+k},x_n)=0$   I proved that $\Rightarrow$ is true,indeed if $(x_n)$ is Cauchy then for all $\varepsilon&gt;0,\exists n_0\in\mathbb{N}, \forall p,q\geq n, d(x_p,x_q)&lt;\varepsilon$ it still right for all $ n\geq n_0$ and $m=n+k&gt;n\geq n_0$   But I don't know if $\Leftarrow$ is true ? "Whether" Vs. "If" Could someone please help me with these sentences? I need to know  Which one doesn’t sound natural? Which one is formal and which one is not?   A - I don’t know whether this word fits in the sentence. B - I don’t know if this word fits in the sentence.   C - I don’t know whether or not this word fits in the sentence. D - I don’t know if or not this word fits in the sentence.   E - I don’t know whether this word fits in the sentence or not. F - I don’t know if this word fits in the sentence or not.  For me only D doesn't work and sounds not idiomatic. Meanwhile for me all of these sentences can be used in both written and spoken languages. Do you confirm me? Check the uniform convergence of series of functions Check that given series converges uniformly for $x\in(-\pi,\pi)$ or not  1) $\sum_{n=1}^{\infty} (\frac{x}{n})^n$  2) $\sum_{n=1}^{\infty}\frac{1}{((x+\pi)n)^2}$  first series is power series so I find the radius of convergence that comes $R=e$ which is inside the given set so I am not able to give the final conclusion. after this I were thinking to apply $M_n$ test , but I am not able to find $M_n$. Please help to solve this problem.