Find the expectation of vertices
up vote
0
down vote
favorite
Question: A point is chosen uniformly at random from the triangle in the plane with vertices (0,0), (1,0), (0,2). Let X be the x-coordinate of this point, and let Y be the y-coordinate of this point.
$$Compute: E(XY^2)$$
I know that $E(XY^2) = E(X)*E(Y^2)$ but I don't know how to compute these two numbers. Could anyone point me in the right direction?
probability uniform-distribution expected-value
edited Dec 4 at 16:42
gt6989b
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
add a comment |
up vote
0
down vote
favorite
Question: A point is chosen uniformly at random from the triangle in the plane with vertices (0,0), (1,0), (0,2). Let X be the x-coordinate of this point, and let Y be the y-coordinate of this point.
$$Compute: E(XY^2)$$
I know that $E(XY^2) = E(X)*E(Y^2)$ but I don't know how to compute these two numbers. Could anyone point me in the right direction?
probability uniform-distribution expected-value
edited Dec 4 at 16:42
gt6989b
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Question: A point is chosen uniformly at random from the triangle in the plane with vertices (0,0), (1,0), (0,2). Let X be the x-coordinate of this point, and let Y be the y-coordinate of this point.
$$Compute: E(XY^2)$$
I know that $E(XY^2) = E(X)*E(Y^2)$ but I don't know how to compute these two numbers. Could anyone point me in the right direction?
probability uniform-distribution expected-value
edited Dec 4 at 16:42
gt6989b
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
Question: A point is chosen uniformly at random from the triangle in the plane with vertices (0,0), (1,0), (0,2). Let X be the x-coordinate of this point, and let Y be the y-coordinate of this point.
$$Compute: E(XY^2)$$
I know that $E(XY^2) = E(X)*E(Y^2)$ but I don't know how to compute these two numbers. Could anyone point me in the right direction?
probability uniform-distribution expected-value
probability uniform-distribution expected-value
edited Dec 4 at 16:42
gt6989b
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
edited Dec 4 at 16:42
gt6989b
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
edited Dec 4 at 16:42
gt6989b
32.7k22451
edited Dec 4 at 16:42
gt6989b
32.7k22451
edited Dec 4 at 16:42
gt6989b
32.7k22451
32.7k22451
asked Dec 4 at 16:32
Zazmadze
12
asked Dec 4 at 16:32
Zazmadze
12
asked Dec 4 at 16:32
Zazmadze
12
12
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
Your $(X,Y)$ are distributed uniform over that triangle $T$. Can you write down their pdf $f(x,y)$? (Remember that $iint_T f(x,y) dxdy = 1.$)
After you do that, the result is
$$
mathbb{E}left[XY^2right] = iint_T xy^2 f(x,y)dxdy.
$$
answered Dec 4 at 16:42
gt6989b
32.7k22451
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',
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%2f3025791%2ffind-the-expectation-of-vertices%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
up vote
1
down vote
Your $(X,Y)$ are distributed uniform over that triangle $T$. Can you write down their pdf $f(x,y)$? (Remember that $iint_T f(x,y) dxdy = 1.$)
After you do that, the result is
$$
mathbb{E}left[XY^2right] = iint_T xy^2 f(x,y)dxdy.
$$
answered Dec 4 at 16:42
gt6989b
32.7k22451
add a comment |
up vote
1
down vote
Your $(X,Y)$ are distributed uniform over that triangle $T$. Can you write down their pdf $f(x,y)$? (Remember that $iint_T f(x,y) dxdy = 1.$)
After you do that, the result is
$$
mathbb{E}left[XY^2right] = iint_T xy^2 f(x,y)dxdy.
$$
answered Dec 4 at 16:42
gt6989b
32.7k22451
add a comment |
up vote
1
down vote
up vote
1
down vote
Your $(X,Y)$ are distributed uniform over that triangle $T$. Can you write down their pdf $f(x,y)$? (Remember that $iint_T f(x,y) dxdy = 1.$)
After you do that, the result is
$$
mathbb{E}left[XY^2right] = iint_T xy^2 f(x,y)dxdy.
$$
answered Dec 4 at 16:42
gt6989b
32.7k22451
Your $(X,Y)$ are distributed uniform over that triangle $T$. Can you write down their pdf $f(x,y)$? (Remember that $iint_T f(x,y) dxdy = 1.$)
After you do that, the result is
$$
mathbb{E}left[XY^2right] = iint_T xy^2 f(x,y)dxdy.
$$
answered Dec 4 at 16:42
gt6989b
32.7k22451
answered Dec 4 at 16:42
gt6989b
32.7k22451
answered Dec 4 at 16:42
gt6989b
32.7k22451
answered Dec 4 at 16:42
gt6989b
32.7k22451
32.7k22451
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3025791%2ffind-the-expectation-of-vertices%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
