what is the expectation of this random variable?
$begingroup$
Suppose X is an Hyper Geometric random variable with parameters w,b and n, that is, X ~ HGeom(w,b,n).
And suppose Y = $Xchoose2$
, what is E(Y)? Using the sum of probability times the value of Y yields a very complicated formula, there should be some clever way to get the result. Could some one help with this?
Thanks.
probability expected-value
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
$endgroup$
add a comment |
$begingroup$
Suppose X is an Hyper Geometric random variable with parameters w,b and n, that is, X ~ HGeom(w,b,n).
And suppose Y = $Xchoose2$
, what is E(Y)? Using the sum of probability times the value of Y yields a very complicated formula, there should be some clever way to get the result. Could some one help with this?
Thanks.
probability expected-value
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
$endgroup$
add a comment |
$begingroup$
Suppose X is an Hyper Geometric random variable with parameters w,b and n, that is, X ~ HGeom(w,b,n).
And suppose Y = $Xchoose2$
, what is E(Y)? Using the sum of probability times the value of Y yields a very complicated formula, there should be some clever way to get the result. Could some one help with this?
Thanks.
probability expected-value
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
$endgroup$
Suppose X is an Hyper Geometric random variable with parameters w,b and n, that is, X ~ HGeom(w,b,n).
And suppose Y = $Xchoose2$
, what is E(Y)? Using the sum of probability times the value of Y yields a very complicated formula, there should be some clever way to get the result. Could some one help with this?
Thanks.
probability expected-value
probability expected-value
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
asked Dec 4 '18 at 0:53
wangshuaijiewangshuaijie
1638
1638
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
First, $Y={ X choose 2}=frac{X!}{2!(X-2)!}=frac{X(X-1)(X-2)!}{2!(X-2)!}=frac{X(X-1)}{2}$.
Second, use the fact that for any random variable $X$ and $a, b in mathbb{R}$, $E(aX+b)=aE(X)+b$.
Thirdly, $Var(X)=E(X^{2})-E(X)^{2}$.
So, $E(Y)=E(frac{X(X-1)}{2})=E(frac{X^{2}-X}{2})=frac{E(X^{2})}{2}-frac{E(X)}{2}$
All that is left is for you to find the expectation and variance of $X$ (so that you can find $E(X^{2})$). You can find the formulas in any textbook or online (Wikipedia).
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
$endgroup$
add a comment |
$begingroup$
Guide:
The mean and variace of Hypergeometric should be well known, that is we know the first two moments.
Express $Y$ as a linear function of $X$ and $X^2$ and use linearity of expectation.
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
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%2f3024956%2fwhat-is-the-expectation-of-this-random-variable%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
$begingroup$
First, $Y={ X choose 2}=frac{X!}{2!(X-2)!}=frac{X(X-1)(X-2)!}{2!(X-2)!}=frac{X(X-1)}{2}$.
Second, use the fact that for any random variable $X$ and $a, b in mathbb{R}$, $E(aX+b)=aE(X)+b$.
Thirdly, $Var(X)=E(X^{2})-E(X)^{2}$.
So, $E(Y)=E(frac{X(X-1)}{2})=E(frac{X^{2}-X}{2})=frac{E(X^{2})}{2}-frac{E(X)}{2}$
All that is left is for you to find the expectation and variance of $X$ (so that you can find $E(X^{2})$). You can find the formulas in any textbook or online (Wikipedia).
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
$endgroup$
add a comment |
$begingroup$
First, $Y={ X choose 2}=frac{X!}{2!(X-2)!}=frac{X(X-1)(X-2)!}{2!(X-2)!}=frac{X(X-1)}{2}$.
Second, use the fact that for any random variable $X$ and $a, b in mathbb{R}$, $E(aX+b)=aE(X)+b$.
Thirdly, $Var(X)=E(X^{2})-E(X)^{2}$.
So, $E(Y)=E(frac{X(X-1)}{2})=E(frac{X^{2}-X}{2})=frac{E(X^{2})}{2}-frac{E(X)}{2}$
All that is left is for you to find the expectation and variance of $X$ (so that you can find $E(X^{2})$). You can find the formulas in any textbook or online (Wikipedia).
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
$endgroup$
add a comment |
$begingroup$
First, $Y={ X choose 2}=frac{X!}{2!(X-2)!}=frac{X(X-1)(X-2)!}{2!(X-2)!}=frac{X(X-1)}{2}$.
Second, use the fact that for any random variable $X$ and $a, b in mathbb{R}$, $E(aX+b)=aE(X)+b$.
Thirdly, $Var(X)=E(X^{2})-E(X)^{2}$.
So, $E(Y)=E(frac{X(X-1)}{2})=E(frac{X^{2}-X}{2})=frac{E(X^{2})}{2}-frac{E(X)}{2}$
All that is left is for you to find the expectation and variance of $X$ (so that you can find $E(X^{2})$). You can find the formulas in any textbook or online (Wikipedia).
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
$endgroup$
First, $Y={ X choose 2}=frac{X!}{2!(X-2)!}=frac{X(X-1)(X-2)!}{2!(X-2)!}=frac{X(X-1)}{2}$.
Second, use the fact that for any random variable $X$ and $a, b in mathbb{R}$, $E(aX+b)=aE(X)+b$.
Thirdly, $Var(X)=E(X^{2})-E(X)^{2}$.
So, $E(Y)=E(frac{X(X-1)}{2})=E(frac{X^{2}-X}{2})=frac{E(X^{2})}{2}-frac{E(X)}{2}$
All that is left is for you to find the expectation and variance of $X$ (so that you can find $E(X^{2})$). You can find the formulas in any textbook or online (Wikipedia).
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
edited Dec 4 '18 at 2:37
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
answered Dec 4 '18 at 2:31
Live Free or π HardLive Free or π Hard
479213
479213
add a comment |
add a comment |
$begingroup$
Guide:
The mean and variace of Hypergeometric should be well known, that is we know the first two moments.
Express $Y$ as a linear function of $X$ and $X^2$ and use linearity of expectation.
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
add a comment |
$begingroup$
Guide:
The mean and variace of Hypergeometric should be well known, that is we know the first two moments.
Express $Y$ as a linear function of $X$ and $X^2$ and use linearity of expectation.
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
add a comment |
$begingroup$
Guide:
The mean and variace of Hypergeometric should be well known, that is we know the first two moments.
Express $Y$ as a linear function of $X$ and $X^2$ and use linearity of expectation.
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
Guide:
The mean and variace of Hypergeometric should be well known, that is we know the first two moments.
Express $Y$ as a linear function of $X$ and $X^2$ and use linearity of expectation.
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 4 '18 at 0:57
Siong Thye GohSiong Thye Goh
100k1466117
100k1466117
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%2f3024956%2fwhat-is-the-expectation-of-this-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
