How to find probability with two random values?












0












$begingroup$


How to find probability $P(xi < eta)$ if $xi sim Beta(1,2), eta sim Exp(1))$? They're also independent.






probability probability-theory







share|cite|improve this question











$endgroup$












  • $begingroup$
    What have you tried so far?
    $endgroup$
    – Federico
    Dec 5 '18 at 15:46










  • $begingroup$
    I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
    $endgroup$
    – nutcracker
    Dec 5 '18 at 15:48










  • $begingroup$
    You can start finding the pdf of $xi$ and $eta$
    $endgroup$
    – Federico
    Dec 5 '18 at 15:50










  • $begingroup$
    Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52










  • $begingroup$
    The you identify the set over which to integrate
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52
















0












$begingroup$


How to find probability $P(xi < eta)$ if $xi sim Beta(1,2), eta sim Exp(1))$? They're also independent.






probability probability-theory







share|cite|improve this question











$endgroup$












  • $begingroup$
    What have you tried so far?
    $endgroup$
    – Federico
    Dec 5 '18 at 15:46










  • $begingroup$
    I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
    $endgroup$
    – nutcracker
    Dec 5 '18 at 15:48










  • $begingroup$
    You can start finding the pdf of $xi$ and $eta$
    $endgroup$
    – Federico
    Dec 5 '18 at 15:50










  • $begingroup$
    Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52










  • $begingroup$
    The you identify the set over which to integrate
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52














0












0








0





$begingroup$


How to find probability $P(xi < eta)$ if $xi sim Beta(1,2), eta sim Exp(1))$? They're also independent.






probability probability-theory







share|cite|improve this question











$endgroup$




How to find probability $P(xi < eta)$ if $xi sim Beta(1,2), eta sim Exp(1))$? They're also independent.






probability probability-theory




probability probability-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 5 '18 at 19:09







nutcracker

















asked Dec 5 '18 at 15:43









nutcrackernutcracker

84




84












  • $begingroup$
    What have you tried so far?
    $endgroup$
    – Federico
    Dec 5 '18 at 15:46










  • $begingroup$
    I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
    $endgroup$
    – nutcracker
    Dec 5 '18 at 15:48










  • $begingroup$
    You can start finding the pdf of $xi$ and $eta$
    $endgroup$
    – Federico
    Dec 5 '18 at 15:50










  • $begingroup$
    Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52










  • $begingroup$
    The you identify the set over which to integrate
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52


















  • $begingroup$
    What have you tried so far?
    $endgroup$
    – Federico
    Dec 5 '18 at 15:46










  • $begingroup$
    I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
    $endgroup$
    – nutcracker
    Dec 5 '18 at 15:48










  • $begingroup$
    You can start finding the pdf of $xi$ and $eta$
    $endgroup$
    – Federico
    Dec 5 '18 at 15:50










  • $begingroup$
    Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52










  • $begingroup$
    The you identify the set over which to integrate
    $endgroup$
    – Federico
    Dec 5 '18 at 15:52
















$begingroup$
What have you tried so far?
$endgroup$
– Federico
Dec 5 '18 at 15:46




$begingroup$
What have you tried so far?
$endgroup$
– Federico
Dec 5 '18 at 15:46












$begingroup$
I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
$endgroup$
– nutcracker
Dec 5 '18 at 15:48




$begingroup$
I guess i should try find $int F_{xi}(t)f_{eta}(t)dt$, because both these distributions are absolutely continuos.
$endgroup$
– nutcracker
Dec 5 '18 at 15:48












$begingroup$
You can start finding the pdf of $xi$ and $eta$
$endgroup$
– Federico
Dec 5 '18 at 15:50




$begingroup$
You can start finding the pdf of $xi$ and $eta$
$endgroup$
– Federico
Dec 5 '18 at 15:50












$begingroup$
Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
$endgroup$
– Federico
Dec 5 '18 at 15:52




$begingroup$
Then you know that the law of the couple $(xi,eta)$ is simply given by the product of the pdf's
$endgroup$
– Federico
Dec 5 '18 at 15:52












$begingroup$
The you identify the set over which to integrate
$endgroup$
– Federico
Dec 5 '18 at 15:52




$begingroup$
The you identify the set over which to integrate
$endgroup$
– Federico
Dec 5 '18 at 15:52










2 Answers
2






active

oldest

votes


















0












$begingroup$

$$
int_0^1 int_0^infty mathbf{1}_{{xi<eta}} 2(1-xi) e^{-eta} ,deta,dxi
= frac2e .
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:28










  • $begingroup$
    @Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
    $endgroup$
    – Federico
    Dec 5 '18 at 18:32










  • $begingroup$
    I mean how do you come from the integral i wrote in the comments above to the double integral written here?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:34










  • $begingroup$
    I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
    $endgroup$
    – Federico
    Dec 5 '18 at 18:35










  • $begingroup$
    I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
    $endgroup$
    – Federico
    Dec 5 '18 at 18:36



















0












$begingroup$

$P(xi < eta)=int_{0}^{1} int_{xi}^{infty} 2e^{-eta}(1-xi) text{d}eta text{d} xi = frac{2}{e}$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:29











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027219%2fhow-to-find-probability-with-two-random-values%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









0












$begingroup$

$$
int_0^1 int_0^infty mathbf{1}_{{xi<eta}} 2(1-xi) e^{-eta} ,deta,dxi
= frac2e .
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:28










  • $begingroup$
    @Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
    $endgroup$
    – Federico
    Dec 5 '18 at 18:32










  • $begingroup$
    I mean how do you come from the integral i wrote in the comments above to the double integral written here?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:34










  • $begingroup$
    I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
    $endgroup$
    – Federico
    Dec 5 '18 at 18:35










  • $begingroup$
    I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
    $endgroup$
    – Federico
    Dec 5 '18 at 18:36
















0












$begingroup$

$$
int_0^1 int_0^infty mathbf{1}_{{xi<eta}} 2(1-xi) e^{-eta} ,deta,dxi
= frac2e .
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:28










  • $begingroup$
    @Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
    $endgroup$
    – Federico
    Dec 5 '18 at 18:32










  • $begingroup$
    I mean how do you come from the integral i wrote in the comments above to the double integral written here?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:34










  • $begingroup$
    I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
    $endgroup$
    – Federico
    Dec 5 '18 at 18:35










  • $begingroup$
    I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
    $endgroup$
    – Federico
    Dec 5 '18 at 18:36














0












0








0





$begingroup$

$$
int_0^1 int_0^infty mathbf{1}_{{xi<eta}} 2(1-xi) e^{-eta} ,deta,dxi
= frac2e .
$$






share|cite|improve this answer









$endgroup$



$$
int_0^1 int_0^infty mathbf{1}_{{xi<eta}} 2(1-xi) e^{-eta} ,deta,dxi
= frac2e .
$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 5 '18 at 15:49









FedericoFederico

4,899514




4,899514












  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:28










  • $begingroup$
    @Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
    $endgroup$
    – Federico
    Dec 5 '18 at 18:32










  • $begingroup$
    I mean how do you come from the integral i wrote in the comments above to the double integral written here?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:34










  • $begingroup$
    I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
    $endgroup$
    – Federico
    Dec 5 '18 at 18:35










  • $begingroup$
    I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
    $endgroup$
    – Federico
    Dec 5 '18 at 18:36


















  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:28










  • $begingroup$
    @Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
    $endgroup$
    – Federico
    Dec 5 '18 at 18:32










  • $begingroup$
    I mean how do you come from the integral i wrote in the comments above to the double integral written here?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:34










  • $begingroup$
    I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
    $endgroup$
    – Federico
    Dec 5 '18 at 18:35










  • $begingroup$
    I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
    $endgroup$
    – Federico
    Dec 5 '18 at 18:36
















$begingroup$
What is the theoretical rule to count these probabilities?
$endgroup$
– nutcracker
Dec 5 '18 at 18:28




$begingroup$
What is the theoretical rule to count these probabilities?
$endgroup$
– nutcracker
Dec 5 '18 at 18:28












$begingroup$
@Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
$endgroup$
– Federico
Dec 5 '18 at 18:32




$begingroup$
@Daniil what do you mean? How to find the pdf's? That's the definition of beta and exponential distribution. How to compute the integral? Well, Fubini might come in handy...
$endgroup$
– Federico
Dec 5 '18 at 18:32












$begingroup$
I mean how do you come from the integral i wrote in the comments above to the double integral written here?
$endgroup$
– nutcracker
Dec 5 '18 at 18:34




$begingroup$
I mean how do you come from the integral i wrote in the comments above to the double integral written here?
$endgroup$
– nutcracker
Dec 5 '18 at 18:34












$begingroup$
I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
$endgroup$
– Federico
Dec 5 '18 at 18:35




$begingroup$
I don't know what the integral you wrote means. Maybe tell us what $F$ and $f$ are
$endgroup$
– Federico
Dec 5 '18 at 18:35












$begingroup$
I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
$endgroup$
– Federico
Dec 5 '18 at 18:36




$begingroup$
I explained in the comments above the procedure. 1) find the pdf. 2) take the product measure. 3) integrate over the correct set
$endgroup$
– Federico
Dec 5 '18 at 18:36











0












$begingroup$

$P(xi < eta)=int_{0}^{1} int_{xi}^{infty} 2e^{-eta}(1-xi) text{d}eta text{d} xi = frac{2}{e}$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:29
















0












$begingroup$

$P(xi < eta)=int_{0}^{1} int_{xi}^{infty} 2e^{-eta}(1-xi) text{d}eta text{d} xi = frac{2}{e}$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:29














0












0








0





$begingroup$

$P(xi < eta)=int_{0}^{1} int_{xi}^{infty} 2e^{-eta}(1-xi) text{d}eta text{d} xi = frac{2}{e}$






share|cite|improve this answer









$endgroup$



$P(xi < eta)=int_{0}^{1} int_{xi}^{infty} 2e^{-eta}(1-xi) text{d}eta text{d} xi = frac{2}{e}$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 5 '18 at 16:01









Legend KillerLegend Killer

1,584523




1,584523












  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:29


















  • $begingroup$
    What is the theoretical rule to count these probabilities?
    $endgroup$
    – nutcracker
    Dec 5 '18 at 18:29
















$begingroup$
What is the theoretical rule to count these probabilities?
$endgroup$
– nutcracker
Dec 5 '18 at 18:29




$begingroup$
What is the theoretical rule to count these probabilities?
$endgroup$
– nutcracker
Dec 5 '18 at 18:29


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027219%2fhow-to-find-probability-with-two-random-values%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Wiesbaden

Image
Wappen Deutschlandkarte 50.0825 8.24 117 Koordinaten: 50° 5′  N , 8° 14′  O Basisdaten Bundesland: Hessen Regierungsbezirk: Darmstadt Höhe: 117 m ü. NHN Fläche: 203,93 km 2 Einwohner: 278.654 (31. Dez. 2017) [1] Bevölkerungsdichte: 1366 Einwohner je km 2 Postleitzahlen: 65183–65207, 55246, 55252 Vorlage:Infobox Gemeinde in Deutschland/Wartung/PLZ enthält Text Vorwahlen: 0611, 06122, 06127, 06134 Kfz-Kennzeichen: WI Gemeindeschlüssel: 06 4 14 000 LOCODE: DE WIB NUTS: DE714 Stadtgliederung: 26 Ortsbezirke Adresse der Stadtverwaltung: Schlossplatz 6 65183 Wiesbaden Webpräsenz: www.wiesbaden.de Oberbürgermeister: Sven Gerich (SPD) Lage der Landeshauptstadt Wiesbaden in Hessen und im Regierungsbezirk Darmstadt Offizielles Logo der Landeshauptstadt Wiesbaden Flagge der Landeshauptstadt Wiesbaden Wiesbaden is
Read more

Marschland

Image
Kilometerweite Marsch in den Vier- und Marschlanden am Elbdeich Die Wedeler Marschlandschaft in Schleswig-Holstein Der Hadelner Kanal zur Entwässerung der Marsch Die tief gelegene Marsch und ein Entwässerungskanal Das Schöpfwerk Otterndorf im Land Hadeln zur Entwässerung der Medem verfügte damals bereits über die größte Kreiselpumpe Europas. Das Schöpfwerk in Neuhaus für die Aue und des Neuhaus-Bülkauer Kanals Als Marsch(land) (v. niederdt., altsächs. mersc ) – auch Masch , Mersch oder Schwemmland genannt – bezeichnet man eine nacheiszeitlich entstandene geomorphologische Landform im Gebiet der nordwestdeutschen Küsten und Flüsse sowie vergleichbare Landformen weltweit. Inhaltsverzeichnis 1 Landschaft 2 Entstehung 3 Marschböden 4 Nutzung 5 Marschgebiete in Deutschland 6 Siehe auch 7 Literatur 8 Weblinks 9 Einzelnachweise Landschaft | Marschen sind generell flache Landstriche ohne natürliche Erhebungen. Si
Read more

Dieringhausen

Image
Dieringhausen Stadt Gummersbach 50.982777777778 7.5316666666667 165 Koordinaten: 50° 58′ 58″  N , 7° 31′ 54″  O Höhe: 165  (160–245)  m Einwohner: 5055  (30. Jun. 2016) Postleitzahl: 51645 Vorwahl: 02261 Lage von Dieringhausen in Gummersbach Im Hohl ca. 1927–1930 Ansicht von Südwesten bei Bünghausen Dieringhausen (im örtlichen Dialekt Dierkesen ) ist ein Ortsteil von Gummersbach im Oberbergischen Kreis, Regierungsbezirk Köln, Nordrhein-Westfalen (Deutschland). Inhaltsverzeichnis 1 Geographie 2 Geschichte 3 Kultur 3.1 Sehenswürdigkeiten 3.2 Regelmäßige Veranstaltungen 4 Infrastruktur und Wirtschaft 4.1 Verkehr 4.1.1 Schienen- und Busverkehr 4.1.2 Straßen 4.2 Öffentliche Einrichtungen 4.2.1 Schulen und Bildungseinrichtungen 4.2.2 Kirchliche Einrichtungen 5 Persönlichkeiten 5.1 In Dieringhausen geboren 5.2 In Dieringhausen gelebt 6 Einzelnachweise 7
Read more