Expected value of lottery drawing by using the Indicator Random Variable?
$begingroup$
The question states:
In a lottery 5 number are chosen from the set {1,..,90} without replacement. We order the 5 numbers in increasing order and we denote by X the number of times the difference between two neighboring numbers is 1.
I included a picture of my attempt and I think I might've messed up since the numbers are ordered.
enter image description here
probability statistics expected-value
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
$endgroup$
add a comment |
$begingroup$
The question states:
In a lottery 5 number are chosen from the set {1,..,90} without replacement. We order the 5 numbers in increasing order and we denote by X the number of times the difference between two neighboring numbers is 1.
I included a picture of my attempt and I think I might've messed up since the numbers are ordered.
enter image description here
probability statistics expected-value
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
$endgroup$
add a comment |
$begingroup$
The question states:
In a lottery 5 number are chosen from the set {1,..,90} without replacement. We order the 5 numbers in increasing order and we denote by X the number of times the difference between two neighboring numbers is 1.
I included a picture of my attempt and I think I might've messed up since the numbers are ordered.
enter image description here
probability statistics expected-value
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
$endgroup$
The question states:
In a lottery 5 number are chosen from the set {1,..,90} without replacement. We order the 5 numbers in increasing order and we denote by X the number of times the difference between two neighboring numbers is 1.
I included a picture of my attempt and I think I might've messed up since the numbers are ordered.
enter image description here
probability statistics expected-value
probability statistics expected-value
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
asked Dec 9 '18 at 21:57
Matt WilburMatt Wilbur
11
11
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Order cannot matter: it affects the numerator and denominator by the same factor of $5!$
So an expectation of $(5 times 4)times dfrac{89}{90times 89} = dfrac29$, which is what you found, looks correct
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
$endgroup$
add a comment |
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3033078%2fexpected-value-of-lottery-drawing-by-using-the-indicator-random-variable%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Order cannot matter: it affects the numerator and denominator by the same factor of $5!$
So an expectation of $(5 times 4)times dfrac{89}{90times 89} = dfrac29$, which is what you found, looks correct
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
$endgroup$
add a comment |
$begingroup$
Order cannot matter: it affects the numerator and denominator by the same factor of $5!$
So an expectation of $(5 times 4)times dfrac{89}{90times 89} = dfrac29$, which is what you found, looks correct
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
$endgroup$
add a comment |
$begingroup$
Order cannot matter: it affects the numerator and denominator by the same factor of $5!$
So an expectation of $(5 times 4)times dfrac{89}{90times 89} = dfrac29$, which is what you found, looks correct
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
$endgroup$
Order cannot matter: it affects the numerator and denominator by the same factor of $5!$
So an expectation of $(5 times 4)times dfrac{89}{90times 89} = dfrac29$, which is what you found, looks correct
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
answered Dec 19 '18 at 18:27
HenryHenry
99.9k480165
99.9k480165
add a comment |
add a comment |
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3033078%2fexpected-value-of-lottery-drawing-by-using-the-indicator-random-variable%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
