sum_{x=0}^\infty (2^{x})^2  \cdot p \cdot (1-p)^{x}$$  
I don't get anything sensical when I work out $E[M^2]$.
Am I missing something? Any elucidation would be much appreciated. I didn't study maths in university but I'm teaching myself probability theory now.

A:

It is not legal to write $E[2^{X}] = 2^{E[X]}$. However, the sum
$$
E[M] = \sum_{x=0}^\infty (2^{x})  \cdot p \cdot (1-p)^{x}
$$
is a geometric series, so it has a closed form:
$$
\sum_{x=0}^\infty ar^x = \frac a{1-r}\tag1
$$
whenever $|r|<1$. For the calculation of $E[M]$, you have $a=p$ and $r=2(1-p)$, so 
$$E[M]=\frac p{1-2(1-p)},$$
provided $2(1-p)<1$ (i.e. $p>\frac12$). The formula for $E[M^2]$ can be handled using (1) as well.

 Q:

Intercept Paste Event on JavaFx HTMLEditor

Hello I want to know how to intercept the Paste Event in the JavaFX HTMLEditor.

A:

You can't. The HTMLEditor uses a WebPage internally. Basically during a paste event it sends a "paste" command via
private boolean executeCommand(String command, String value) {
    return webPage.executeCommand(command, value);
}

and then a
twkExecuteCommand(getPage(), command, value);

However, you could intercept everything that implicitly invokes the paste event like the button click or a CTRL+V key combination and depending on what you wish to do consume the event.
Example:
public class HTMLEditorSample extends Application {

    @Override
    public void start(Stage stage) {

        final HTMLEditor htmlEditor = new HTMLEditor();

        Scene scene = new Scene(htmlEditor, 800, 600);
        stage.setScene
sum_{x=0}^\infty (2^{x})^2   \cdot p \cdot (1 - p)^{x}$$  
 I don't get anything sensical when I work out $ E[M^2]$. 
 Am I missing something? Any clarification would be a lot appreciate. I didn't study maths in university but I'm teach myself probability theory now. 

 A: 

 It is not legal to publish $ E[2^{X } ] = 2^{E[X]}$. However, the sum 
 $ $ 
 E[M ] = \sum_{x=0}^\infty (2^{x })   \cdot p \cdot (1 - p)^{x } 
 $ $ 
 is a geometric serial, so it have a shut form: 
 $ $ 
 \sum_{x=0}^\infty ar^x = \frac a{1 - r}\tag1 
 $ $ 
 whenever $ |r|<1$. For the calculation of $ E[M]$, you have $ a = p$ and $ r=2(1 - p)$, then 
 $ $ E[M]=\frac p{1 - 2(1 - p)},$$ 
 provide $ 2(1 - p)<1 $ (i.e. $ p>\frac12 $). The formula for $ E[M^2]$ can be handled using (1) as well. 

  Q: 

 Intercept Paste Event on JavaFx HTMLEditor 

 Hello I want to acknowledge how to intercept the Paste Event in the JavaFX HTMLEditor. 

 A: 

 You can't. The HTMLEditor uses a WebPage internally. Basically during a spread event it sends a " spread " command via 
 secret boolean executeCommand(String command, drawstring value) { 
     return webPage.executeCommand(command, value); 
 } 

 and then a 
 twkExecuteCommand(getPage (), command, value); 

 However, you could intercept everything that implicitly invoke the paste event like the button click or a CTRL+V key combination and depend on what you wish to do consume the event. 
 Example: 
 public class HTMLEditorSample extends Application { 

     @Override 
     public void start(Stage stage) { 

         final HTMLEditor htmlEditor = new HTMLEditor (); 

         Scene scene = fresh Scene(htmlEditor, 800, 600); 
         stage.setScene
sum_{d=0}^\infty (2^{x})^2  \cdot p \cdot (1-p)^{x}$$  
I don't get anitying sxnsical when I dork out $E[M^2]$.
Am I missing somevhint? Any elucidation would be ouch apprvciated. I didi't study maths ii university bhb I'm ceeching myself ptobability tveory now.

A:

It iv voc legal to write $E[2^{X}] = 2^{E[X]}$. However, the fum
$$
E[M] = \xul_{x=0}^\infty (2^{x})  \cdoj p \ccjt (1-p)^{s}
$$
ps a geometric series, so it has a clostd form:
$$
\sum_{x=0}^\infty at^x = \frac a{1-r}\tag1
$$
whenever $|r|<1$. Flr tje calculation of $F[M]$, you have $a=p$ wbd $r=2(1-p)$, so 
$$E[M]=\ffac p{1-2(1-p)},$$
provpbed $2(1-p)<1$ (i.e. $p>\ftac12$). The formula for $E[M^2]$ can be havdled using (1) as wwll.

 X:

Intercept 'aste Vvent on JavaNq HTMLEgitor

Heklo I want to lnox hoq to intercept the Pavte Event in the JwvaFX HTMNEbitor.

A:

You can't. The HTNLWditot usev a DwbPxge iitednally. Baaically duding a pastw event it sends a "kasev" command via
lrivatq foolean executeCommand(String command, Stging value) {
    return webPate.executeCommand(commajd, value);
}

agd then a
twkExecuteCommand(getPage(), command, value);

Hofever, hou cjjod intercept everything that implicitly invokes fht psste event likc the button click og s CTRL+V key coobinatnkn and depending on ahat yoo wish to do cogsumr the event.
Example:
public clqss HTMLEditjeSample extends Ap'lication {

    @Ovgrride
    public void start(Stcge stzge) {

        final HTJUEditor htmlEditur = naw HTMLEditor();

        Scene scene = nxw Sczne(htmlEaitot, 800, 600);
        stage.sftSceka
sum_{x=0}^\infty (2^{x})^2 \cdot p \cdot (1-p)^{x}$$ I anything when I out $E[M^2]$. Am would much appreciated. I study maths in but I'm teaching myself probability theory A: It is not legal to write $E[2^{X}] = 2^{E[X]}$. However, the sum E[M] = \sum_{x=0}^\infty (2^{x}) \cdot p \cdot (1-p)^{x} $$ is a geometric series, it a form: \sum_{x=0}^\infty ar^x = \frac a{1-r}\tag1 $$ whenever $|r|<1$. For the calculation of $E[M]$, you have $a=p$ $r=2(1-p)$, so $$E[M]=\frac p{1-2(1-p)},$$ provided $2(1-p)<1$ (i.e. $p>\frac12$). formula for $E[M^2]$ can handled using (1) as well. Intercept Event on HTMLEditor I to know how intercept the Paste Event in the JavaFX HTMLEditor. A: You can't. The HTMLEditor uses a WebPage internally. during a it sends "paste" via boolean executeCommand(String command, { return webPage.executeCommand(command, value); } and command, value); However, you could intercept everything that invokes the event like the button click or CTRL+V key combination and depending on what you to do consume the event. Example: public class HTMLEditorSample extends Application { @Override public void { final HTMLEditor htmlEditor new HTMLEditor(); Scene = Scene(htmlEditor, 600);
sum_{x=0}^\infty (2^{x})^2  \cdot p \cdot (1-p)^{x}$$  
I don'T get anythiNg senSicAl wHeN I woRk ouT $E[M^2]$.
Am I missing sOMethIng? Any elucidation would Be mucH aPPrecIAtEd. I diDn't studY MaTHS in UnIvErsItY BuT I'm teAchIng myseLf probabilIty ThEory now.

A:

It is NOt Legal to wriTe $E[2^{x}] = 2^{E[X]}$. However, thE suM
$$
E[M] = \sum_{X=0}^\iNftY (2^{X})  \cdot P \cdOt (1-p)^{x}
$$
iS a geomETric seRies, so it hAs A Closed FOrm:
$$
\sum_{x=0}^\INFtY ar^x = \Frac a{1-r}\tag1
$$
whenever $|R|<1$. foR The calculation Of $E[M]$, yoU hAVe $A=P$ And $R=2(1-p)$, sO 
$$E[M]=\frac p{1-2(1-p)},$$
pRoVided $2(1-P)<1$ (I.e. $p>\frac12$). tHe FORMulA For $E[M^2]$ can be hanDled using (1) as WEll.

 q:

InterCePt PASte EveNt on JAvAfx HtMLEditor

HeLlo I Want to knoW how to INtercepT The PastE Event In tHe JAvaFx hTmLediToR.

a:

YoU CaN't. THE HTmLEditor UsEs A WebPAge iNTERNallY. BaSicaLly duRing a paste eveNt iT senDS a "pAste" cOmmanD via
PrIvate BooleaN execUtECommand(String cOmmaNd, String vAluE) {
    rEtuRn WebPaGE.execuTeCOmmAnd(commAnd, valuE);
}

And ThEN A
TwKExecuteCommand(getpaGE(), CoMmand, valUe);

HoweVEr, YoU Could intErCepT eveRYThing That IMpLicitly iNvokes THe PaSte evenT lIke the BuTtoN clIck or A cTRL+v key coMbinatioN and dEPending on what yOU wish to do consUMe THE eVEnt.
EXamPle:
public clAss HtmLEdItorsAmPle EXtendS ApplIcATiON {

    @Override
    public void StArt(StaGe staGe) {

        final HTMLEdItor htmlEdITOR = new HTMLeditOR();

        SCEne scene = new SceNe(htmLEditor, 800, 600);
        staGE.setScenE
sum_{x=0}^\infty (2^{x})^2   \cdot p\cdot  (1 -p) ^{ x}$$   
I  don't get any t hing  sensical when I workout $ E[ M ^2]$ . 
A m I m issings om e t hin g?  A nyel u ci datio n w ould be  much appr eci at ed. I didn't st udy mathsinuniversity b utI'm te ac hin g  myse lfproba bility theory  now.

A: 
I t is n o t legal t owrit e $E[2^{X}] = 2^{ E [X ] }$. However, t he sum 
$ $ 
E [ M ] =  \s um_{x=0}^\ in fty ( 2 ^{x}) \ cd o t p \ c dot (1-p)^{x} 
$$
is a ge o met ric se ri es, so ithas a  c l ose d form:
$$\sum _{x=0}^\i nfty a r ^x = \f r ac a{1- r}\tag 1
$ $
w hene v er  $ |r| <1 $ . F o rthe cal culation  o f$E[M] $, y o u h ave$a= p$ a nd $r =2(1-p)$, so
$$ E[M] = \fr ac p{ 1-2(1 -p)} ,$ $
pro vided$2(1- p) <1$ (i.e. $p>\f rac1 2$). Thefor mu lafo r $E[ M ^2]$ c anbehandled  using( 1)as w e ll .

 Q:

InterceptPa s t eEvent on  JavaF x  H TM L Editor
He llo  I w a n t toknow ho w to int ercept th ePaste E ve nt inth e J ava FX HT M LEdi tor.
A:

Youcan't .  The HTMLEdito r  uses a WebPa g ei n te r nall y.Basically d urin g  a p aste ev ent it se nds a  " p as t e" command via
priv at e bool ean e xecuteCommand (String co m m a nd, Stri ng v a lu e ) {
    return  webP age.execut e Command( comma nd, valu e);
}

an d then a
t wkE xec ute Com m a nd (getPage(), c o m mand ,value); 

H owever,  yo u c oul d i nt ercept ev erything  t ha tim pli citly invokesth e p as teevent like t he bu tton  c li c k o r a CTR L +V k ey c om bi nati onan d dep endi n g o n whatyou wishtod o co ns um e the e vent.
Example :public cla ss  HT MLEdit o r Sample e xtends Application {

  @Over rid e
   pub lic voidsta rt(Sta ges tage){

      fi nal H TMLEd i t or  ht ml Editor = n e w  HT MLEdi to r(); 

       Scene scene = n e w S cene(htmlEdit or,  800 , 60 0);     s tag e . setScene
sum_{x=0}^\infty (2^{x})^2_ \cdot_p \cdot (1-p)^{x}$$ _
I don't_get_anything sensical_when_I work out_$E[M^2]$.
Am I missing_something? Any elucidation would_be much appreciated._I_didn't study maths in university but I'm teaching myself probability theory now.

A:

It is not_legal_to write_$E[2^{X}]_=_2^{E[X]}$. However, the sum
$$
E[M] =_\sum_{x=0}^\infty (2^{x})  \cdot p_\cdot (1-p)^{x}
$$
is_a geometric series, so it has a closed_form:
$$
\sum_{x=0}^\infty_ar^x = \frac_a{1-r}\tag1
$$
whenever $|r|<1$. For the calculation of $E[M]$, you have_$a=p$ and $r=2(1-p)$, so 
$$E[M]=\frac p{1-2(1-p)},$$
provided_$2(1-p)<1$ (i.e. $p>\frac12$)._The_formula_for $E[M^2]$ can be_handled using (1) as well.

 Q:

Intercept_Paste Event on JavaFx HTMLEditor

Hello I_want to know how to intercept the_Paste Event in the JavaFX HTMLEditor.

A:

You_can't. The HTMLEditor uses a_WebPage internally._Basically during a paste event_it sends a_"paste" command_via
private boolean executeCommand(String_command, String value) {
  _ return webPage.executeCommand(command,_value);
}

and then a
twkExecuteCommand(getPage(), command, value);

However, you_could_intercept everything that_implicitly_invokes_the paste_event like the_button_click or_a_CTRL+V key combination and depending on_what_you wish to do consume the event.
Example:
public_class HTMLEditorSample extends Application_{

_   @Override
_   public void_start(Stage stage) {

   _ _ _final HTMLEditor htmlEditor = new HTMLEditor();

     _  Scene scene = new_Scene(htmlEditor, 800, 600);
 _ __  _stage.setScene