To what extent can we call a Geometric Distribution a Geometric Density
Does Wolfram Mathworld make a mistake describing a discrete probability distribution with a probability density function?
First of all, am I being crazy in thinking that if $\lambda$ is an eigenvalue of $AB$, where $A$ and $B$ are both $N \times N$ matrices (not necessarily invertible), then $\lambda$ is also an eigenvalue of $BA$?  If it's not true, then under what conditions is it true or not true?  If it is true, can anyone point me to a citation?  I couldn't find it in a quick perusal of Horn &amp; Johnson.  I have seen a couple proofs that the characteristic polynomial of $AB$ is equal to the characteristic polynomial of $BA$, but none with any citations.  A trivial proof would be OK, but a citation is better. Is the trace of inverse matrix convex? Number of ways to choose $n$ balls from $3n$ balls, distinguishable/indistinguishable. Is there a way to reorganize the fields/attributes in a data extension?  I've added some extra fields that relate to other fields in that extension.   I haven't found a way to regroup those fields. File and directory comparison tool? I'm looking for something that will compare directories and files like Beyond Compare does for windows.  Its mainly for use of source control, but I need to use it for deployment as well. Router to router setup works fine with straight cable up to 2-3 meter it is not working for 45 meter why? I have a layout similar to this:  &lt;div id="..."&gt;&lt;img src="..."&gt;&lt;/div&gt;   and would like to use a jQuery selector to select the child img inside the div on click.  To get the div, I've got this selector:  $(this)   How can I get the child img using a selector? Are there any holidays in Middle Earth, except Yule, Lithe, New Year in Gondor and Durin's Day? How to call a function on a directive scope from the controller Is there an easy way to disable this laptop's touchpad? Specifically, I'm on a . I'd like to disable the  so that I can re-enable if my mouse were to run out of batteries (so physically breaking the connection to the motherboard or uninstalling the driver will not be the best options). In the Control Panel, when I go to "Mouse" and find the touch pad, there is no disable option. Any ideas?  Edit: I am on Windows 7. There is a driver on the Dell site that might allow an option to disable it, but I cannot install it on Windows 7. Inverse of sum of exponential random variables (mean and variance) Assume $X_1,X_2, \dots , X_n$ following the exponential distribution with mean $\theta &gt; 0 $ and the statistic: $$ T = \sum\limits_{i = 1}^n X_i $$  I know that the sum of exponential random variables follows the Gamma distribution, but I cannot infer anything about the inverse of the sum $\frac{1}{T}$. My guess would be that: $$ E\left[\frac{1}{T}\right] = \frac{1}{\theta} \quad \text{and} \quad V\left[ \frac{1}{T} \right] = \frac{1}{\theta^2} $$ but why? Netgear WNA3100 wifi dongle not recognized Icons of Meta.SE and Stack Apps have gone missing what is/are the purpose(s) of inline? The question is to show that for any $x,y \in\Re^n$  $||x+y||\cdot||x-y||\le||x||^2+||y||^2$  with equality if and only if $\langle x,y \rangle= 0.$  I have that $||x+y||^2=||x||^2+2 \langle x,y \rangle+||y||^2$ , which helps me prove equality but I'm lost on how to show this and show that the inequality part. What is the meaning of the integral of position? Jerk, $j(t)=\dddot x(t)$, acceleration, $a(t)=\ddot x(t)$ and velocity, $v(t)=\dot x(t)$ are derivatives of position, $x(t)$. What is the meaning of the integral of position?  For example, one could write  $$\int x \mathrm{d}t = \int x \frac{\mathrm{d}t}{\mathrm{d}x}\mathrm{d}x = \int x\frac{1}{v} \mathrm{d}x$$  which reminds the equation for . Cyclic Group Generators of Order $n$ Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain How do you name your ViewModel classes? says that the number of different monomials of degree $M$ in $N$ variables is $$\frac{(M+N-1)!}{M!(N-1)!}\; .$$ Can anyone explain why this is true?