Simple question about MVN pdf. I understand the domain to be [0,1]. However, why does scipy.stats.multivariate_normal.pdf output values above this range. E.g.  action = np.array(               [0.0771532, -0.0921249, 0.155535, 0.110629, -0.0750895, 0.0490313, 0.0416572, -0.0489283, 0.117888, 0.0104795, 0.0261741, -0.193333, -0.199992, -0.119793, -0.00147295, 0.0347881, -0.0862036, -0.0163956, -0.011512, -0.0051254, 0.0744867, -0.0815146, 0.00417948, 0.0575905, 0.0776339, -0.174205, -0.00825691, 0.0330421, -0.163067, 0.0111632, 0.104023, -0.0618963, -0.171926, -0.0930436, 0.0505307, -0.0134338, -0.100431, -0.133168, 0.146748, 0.120166],               dtype=np.float64).reshape((10,4)) mean = np.array(             [-0.0125206, -0.019085, 0.0512585, -0.0105176,              -0.0125206, -0.019085, 0.0512585, -0.0105176,              -0.0125206, -0.019085, 0.0512585, -0.0105176,              -0.0125206, -0.019085, 0.0512585, -0.0105176,              -0.0125207, -0.019085, 0.0512585, -0.0105176,              -0.0125207, -0.0190849, 0.0512585, -0.0105176,              -0.0125207, -0.0190849, 0.0512585, -0.0105176,              -0.0125207, -0.0190849, 0.0512585, -0.0105176,              -0.0125207, -0.0190849, 0.0512585, -0.0105176,              -0.0125207, -0.0190849, 0.0512585, -0.0105177,              ],             dtype=np.float64).reshape((10,4)) std = np.array(            [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,             0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,             0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,             0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1],            dtype=np.float64).reshape((10,4))   res4 = multivariate_normal.pdf(action[0,:],mean[0,:],np.diag(std[0,:]**2))  print("scipy normal pdf:\n",res4)  #&gt;&gt;&gt; 36.17148   Edit: It is clear thanks to a_statistician that $\int_x pdf(x) = 1$. Now how to find $P(X=x, M=\mu,\Sigma=\sigma)$? I am aware that the probability of any particular data point is zero if the set of possible values is continuous.
On the , there is this line:      $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)    How can a value $&gt;1$ be OK? I thought all probability values were expressed in the range $0 \leq p \leq 1$. Furthermore, given that it is possible to have such a value, how is that value obtained in the example shown on the page?
What are homologous chromosomes? Answers to a  mention that it is illegal for a US citizen to enter/leave their home country on a foreign passport. However this raises the following questions:   What is the maximum prescribed penalty for violating these rules? Are US immigration officials known for actually applying the penalty? E.g. the Cuba embargo banning visits to Cuba was almost never enforced, so it's possible this law is ignored as well. How do you "OR" criteria together when using a criteria query with hibernate? I posted a question recently regarding my Windows 10 upgrade which ended up with a black screen and cursor.   I reverted back to Windows 8.1 using the "Revert to previous build" option in recovery, and all seems fine, except that Virtualisation is disabled.  I tried to open BIOS settings but it just boots into Windows. I've tried the usual F2 key and Shift F2, all the other F keys, tried pressing B and Shift+B but no luck.  I tried pressing the Lenovo key on the laptop when it is powered down, which shows a menu to either boot into BIOS, recovery, or show boot menu. I choose BIOS and it just boots into Windows.  I tried going into advanced startup options from Windows (Shift+Restart) and choosing "UEFI FIRMWARE SETTINGS" but it just reboots back into Windows.  Before the Windows 10 upgrade it was working perfectly.  Lenovo G580 laptop - Core i3 with Intel 4000 graphics. 8GB of RAM and a Crucial MX100 512GB SSD (replaced the original hard drive with this SSD). Bluetooth Broadcom 43142 isn't working Calculate the uncertainty in velocity of electron I got this question in one of my periodic test in coaching, I (seemingly) solved the question but later recognised what mess I did.  So, the question is :      Calculate the uncertainty in velocity of an electron. If the uncertainty in its position is ${10^ {-15}} \; \mathrm m$.   By simple calculations one can see that the answer would be ${5.79\times{10^{10}}} \; \mathrm{m/s}$. However, as one can see, the uncertainty in velocity is greater than the velocity of light then how is that possible or there is some other way to handle such problems.  P.S. I know the concept of dynamic mass but I am not very familiar with it. (I think that would work here, but don't know how?) Issues with win key and right alt key after Windows Update (Polish diacritical signs not working) bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$ We have more than one content management system (eCommerce) running on our site and we want to know would it be wise to separate these systems and run on their own server for better performance, easier to manage and better for security, but our concern is the SEO impact.  Is it better to run site.com/this-is-our-other-platform/ or this-is-our-other-platform.site.com? Onomatopoeia for disgust How come unpolarized light does not undergo destructive interference? As far as I know, unpolarized light is defined as light which has no clear axis of polarization, but electric field vectors in all directions. However, I also know that electric fields can be superpositioned. So this leads me to the conclusion that if unpolarized light has equal $\vec E$ vectors in all directions, they should cancel.   Obviously, though, this is wrong (we've got light!). What's the explanation? Take a look at the following screenshot I took from Google Webmaster Tools "Remove URLs" page:   None of these were performed by me or others who have access to GWT.  How do these removal requests happen without us doing any requests?  Why is that happening?  How to stop that or is there any point in stopping that? What are the advantages of 10-bit monitors? To support 10-bit color the following are needed:   A monitor supporting it. A GPU supporting it (only AMD FirePro and NVIDIA Quadro support this?). Compatible software. Unless I am mistaken there are very few programs out there supporting 10-bit color. Photoshop is a notable example.   The questions are about how 10-bit monitors perform in comparison with 8-bit monitors:   In which situations would a 10-bit monitor give a noticeable advantage over an 8-bit monitor (say, for professional photography)? Have 10-bit monitors been compared against 8-bit monitors based on subjective or objective tests? What were the results? Human eyes can see only 10m colors, so would using a monitor with 1b colors make a difference? 0 ram free on ICS Can't install jdk on Fedora with yum nor with rpm Privilege banner buggy? Or am I just confused? On the main Stack Overflow site, I arrived and had a banner: "Congrats, you've gained the privilege – create wiki posts and 3 other privileges" This confuses me, because I only see two privileges listed at 100%. Is the banner just buggy?  Or is there a better place to see my privileges that the page linked to by that banner? I'm studying special relativity and saw the 2 postulates of Einstein. The most remarkable one for me is the universal speed of light. Einstein postulated that the speed of light in vacuum is the same for all inertial observers, regardless of the motion of the source. But what if we are accelerating and we are changing from one inertial frame to another, how will we observe the speed of light? Is it still the same? I suggest it's not? Because I alread saw a small introduction to general relativity where the light will bend in a gravitational field and therefore also when you accelerate. So does the speed of light change because it bends? Is it possible to use text-overflow:ellipsis on multiline text? When can I make opportunity attacks? What provokes an opportunity attack?  In 3.X moving out of a threatened square, standing up from prone, casting a spell (unless cast defensively), or making a ranged attack provoked, while in 4e moving out of a threatened square or making a ranged/area attack provoked. Let, $X$ be a countable set. Which of the following are true?   There exists metric $d$ on $X$ so that $(X,d)$ is complete. There exists metric $d$ on $X$ so that $(X,d)$ is not complete. There exists metric $d$ on $X$ so that $(X,d)$ is compact. There exists metric $d$ on $X$ so that $(X,d)$ is not compact.   4 is true as we can take discrete metric. Then $\{\{x\}:x \in X\}$ is an open cover containing no finite subcover.  If there exists a compact metric then it would automatically become complete also. Hence if 3 is true, so is 1.  What about 2? Any other comment?