Mixing
What is the expectation of $X$?
0
$begingroup$
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is ?
probability random-variables expected-value
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
$endgroup$
add a comment |
0
$begingroup$
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is ?
probability random-variables expected-value
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
$endgroup$
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
2
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28
add a comment |
0
0
0
$begingroup$
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is ?
probability random-variables expected-value
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
$endgroup$
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is ?
probability random-variables expected-value
probability random-variables expected-value
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
edited Jan 5 at 6:37
Antonios-Alexandros Robotis
9,75241640
9,75241640
asked Jan 5 at 6:33
empty-soulempty-soul
1
asked Jan 5 at 6:33
empty-soulempty-soul
1
asked Jan 5 at 6:33
empty-soulempty-soul
1
1
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
2
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28
add a comment |
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
2
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
2
2
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28
add a comment |
0
active
oldest
votes
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
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%2f3062452%2fwhat-is-the-expectation-of-x%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
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%2f3062452%2fwhat-is-the-expectation-of-x%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
$begingroup$
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level.
$endgroup$
– Clement C.
Jan 5 at 6:58
$begingroup$
i approached this problem as : since we need minimum 2 tosses to get two heads. starting from two tosses we get expectation as 2*(1/4) + 3*(1/8) + 4*(1/16)+ ... and so on. is this a correct way or am i doing something wrong.
$endgroup$
– empty-soul
Jan 5 at 7:03
2
$begingroup$
@empty-soul Add your working in your original post by editing it.
$endgroup$
– StubbornAtom
Jan 5 at 7:11
$begingroup$
@empty-soul: What tools do you have? Do you know Markov chains? Also, are you sure about your probability mass for the case when it takes 4 flips?
$endgroup$
– Michael
Jan 5 at 7:53
$begingroup$
anyone please post an answer.
$endgroup$
– empty-soul
Jan 5 at 16:28