Finding ML(Maximum Likelihood) estimator
Finding the maximum likelihood estimators for this shifted exponential PDF?
Turn off automatic preview in apple mail Is it possible to turn off automatic preview of attachments when composing an e-mail?  NOTE: Yes I know that I can manually ctr+select the attachment and disable preview, but I want this done automatically If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ Probability of continuous random variable What is the C# equivalent of NaN or IsNumeric? Fingerprint GUI not installing in Ubuntu 20.04 I'm trying to install fingerprint-gui on my Lenovo Ideapad 520 having Ubuntu 20.04 on which fingerprint isn't working for now. I tried going directly to Settings → Users → Automatic login and enabled the fingerprint login, but the error is:  Could not access any fingerprint readers Please contact your system administrator for help!  I also tried to install Fingerprint GUI: sudo apt-add-repository ppa:fingerprint/fingerprint-gui &amp;&amp; sudo apt-get update  sudo apt-get install libbsapi policykit-1-fingerprint-gui fingerprint-gui  but encountered this error: E: Package 'policykit-1-fingerprint-gui' has no installation candidate E: Package 'fingerprint-gui' has no installation candidate  What could be the problem here? Real Numbers Raised to Imaginary Powers? What is a real number to the power of an imaginary or complex number? e.g. 3i. I have searched through sites about imaginary numbers, but none seem to say anything about imaginary indices. Examples and explanations would be appreciated. How to know if Google Sheets IMPORTDATA, IMPORTFEED, IMPORTHTML or IMPORTXML functions are able to get data from a resource hosted on a website? Google Sheets has several import functions   IMPORTDATA IMPORTFEED IMPORTHTML IMPORTXML   Sometimes the above functions returns errors like #N/A Imported content is empty and would like to be sure that there isn't a problem with the resource content to be imported.  How do I know if these functions are able to get the content that I looking to import?  I know that there also exist IMPORTRANGE but that function only is able to import content from Google Sheets spreadsheets Word for the situation of being unable to pass opposing pedestrian, as you both start to step same direction Is there a word or expression in English, which describes the situation, when you can't pass a  stranger, who is walking towards you on the street, because you both start to step the same direction?  I'm pretty sure I've heard one once. As I remember, it was including "dancing" reference, but in more specific way. Another word for a troll not on the internet The definition of an internet troll:     In Internet slang, a troll (/ˈtroʊl/, /ˈtrɒl/) is a person who sows   discord on the Internet by starting arguments or upsetting people,   by posting inflammatory,[2] extraneous, or off-topic messages in an   online community (such as a forum, chat room, or blog), either   accidentally[3][4] or with the deliberate intent of provoking readers   into an emotional response[5] or of otherwise disrupting normal   on-topic discussion.[6]      This sense of the word troll and its associated verb trolling are   associated with Internet discourse, but have been used more widely.   Media attention in recent years has equated trolling with online   harassment. For example, mass media has used troll to describe "a   person who defaces Internet tribute sites with the aim of causing   grief to families."[7][8]     What is the equivalent for a person who does this type of thing in real life (non-cyber) troll? Proving an infinite number of primes of the form 6n+1 The proofs given on other sites weren't that clear and used different methods that I have yet to learn.    Prove that there are an infinite number of primes of the form 6n+1.  The hint that was given was: Let p = p1, p2, ..., pk + 1, where p1 = 2, p2 = 3,...pk are the first k primes.  Show that p is prime.  (p1 means p sub 1, p2 means p sub 2, and pk is p sub k.  Wasn't sure how to write it on this.)    Can someone explain this hint on how they came about of p1 = 2, p2=3, etc, and prove this please?    Also, how would the proof change if the form changed?  ("Prove that there are infinite number of primes of the form....") Any good tutorials for learning how to post-process images? I don't really know where to start with post-processing my images. I normally just straighten, crop and sharpen. Do people know of any good resources on the internet for getting a grip with Photoshop and similar tools? What were the rules for capitalising nouns in the 17th and 18th centuries? It seems to have been common practice in the 17th and 18th centuries in English-language sources to capitalise the first letters of nouns, as in  At which Time he prov'd himself the Noah's Dove, that finding himself no Rest anywhere, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his mouth. —  (1685)  Most original sources I can find on the web have used modern rules for capitalisation, so I have a few questions:  Was the practice used for all nouns (Note mouth isn't capitalised in my quotation above.)? When did this practice begin? When and why did it end? I want to upgrade the hard drive in my 2012 Macbook Pro to an SSD. I have the parts, but had a question about how to clone the contents of my current drive so I can install it onto the SSD.  I've seen tutorials where people suggest connecting the new SSD to the Macbook prior to installation and using a Carbon Copy Cloner to clone the drive, and then installing the SSD drive.  My question is, can I do a Time Machine backup of my current hard drive on an external hard drive, install the SSD, and then use the Time Machine backup from the external to transfer it onto the newly installed SSD? Is this the same as using the clone program above? I know that SZ0 makes vertices straightened on the z-axis, but I'm wondering if there's a way to make vertices into a complete circle on the z-axis with a hotkey? A subgroup of a cyclic group is cyclic - Understanding Proof I'm having some trouble understanding the proof of the following theorem  A subgroup of a cyclic group is cyclic  I will list each step of the proof in my textbook and indicate the places that I'm confused and hopefully somewhere out there can clear some things up for me.  Proof Let  G be a cyclic group generated by &quot;$a$&quot; and let H be a subgroup of G. If $H = {\{e\}}$, then $H \text{ = &lt;e&gt;}$ is cyclic. If $H \neq \space {\{e\}}$, then $a^n \in H$ for some $n \in \mathbb{Z}^{+}$. Let $m$ be the smallest integer in $\mathbb{Z}^{+}$ such that $a^m \in H$. We claim that $c = a^m$ generates H; that is, $$H \space = \space &lt;a^m&gt; \space = \space &lt;c&gt;.$$ We must show that every $b \in H$ is a power of c. Since $b \in H$ and $H \leq G$, we have $b = a^n$ for some $n$. Find $q$ and $r$ such that $$ n = mq + r \space \space \space \space for \space \space \space 0 \leq r &lt; m,$$  Alright this is the first part in the proof where I start to get confused. Where does the division algorithm come from and why are we using it? The proof continues as follows:  $$a^n = a^{mq + r} = (a^m)^q \cdot a^r,$$ so $$ a^r = (a^m)^{-q} \cdot a^n.$$ Now since $a^n \in H$, $a^m \in H$, and $H$ is a group, both $(a^m)^{-q}$ and $a^n$ are in $H$. Thus $$(a^m)^{-q} \cdot a^n \in H; \space \space \space \text{that is,} \space \space a^r \in H.$$  This is another point at which I’m a little confused. What exactly about $a^n$ and $a^m$ being elements of $H$ allows us to accept that $(a^m)^{-q}$ and $a^{n}$ are in $H$? The proof continues:  Since $m$ was the smallest positive integer such that $a^m \in H$ and $0$ $\leq r$ $&lt; m$, we must have $r = 0$. Thus $n = qm$ and $$b \space = \space a^n \space = \space (a^m)^q \space = \space c^q,$$ so b is a power of c.  This final step is confusing as well, but I think its just because of the previous parts I was confused about. Any help in understanding this proof would be greatly appreciated Check existence of input argument in a Bash shell script The Crumple-Horned Snorkack is one of various weird and wacky things which Luna Lovegood believes in and most people (especially the ever-rational Hermione) don't. Now we know that Luna is a bit ... odd, and believes in a lot of nonsense; but on the other hand, Hermione's pooh-poohing isn't always to be believed either - Divination, for instance, is a real thing in the Potterverse.  Is it ever established for sure, in canon, in-universe, whether or not Crumple-Horned Snorkacks exist? I have used the websites of SO a lot the past few months because I am busy with a large scale web project. I feel I get better answers here on SO than when I just do a Google search, maybe because I can be more specific here with my problem, and the responses are really fast.  Occasionally when I am not working I try to answer some questions, but the question almost always has an answer which is 'as good as' or 'better' than the answer I would supply.  So my question/answer ratio is about 20/1 something, if not more. When I look at my profile page I see a bucket-load of questions and almost nothing I answered myself.  Is this considered bad behaviour? I can see that this looks a little egoistic.  : One devoted to one's own interests and advancement. Is there any Stack Exchange site where the main topic is literature?  I have tried the English Language site, but it seems that it is not the appropriate site.  Perhaps the writers site would work? But, then again, the main point is different than the one I am searching for. sudo: /etc/sudoers is owned by uid 501, should be 0 To run programs as sudo without password, I edited /etc/sudoers with wrong content.   Then I re-edited it with Mac's default text editor(course sudo cannot be used when /etc/sudoers is wrong).  I tried to run sudo agin, and get this error:   sudo: /etc/sudoers is owned by uid 501, should be 0 sudo: no valid sudoers sources found, quitting   What should I do? I cannot remember the root password (maybe I haven't ever set root password before).