Joint uniform distribution two different intervals
$begingroup$
I have a problem with the following exercise:
X corresponds to the duration of Paul’s commute to work, and Y to the duration of Peter’s. X is uniformly distributed in [15, 25] and Y in [15, 30]. X and Y are assumed
to be independent.
What is the probability that Peter and Paul both take more than 20 minutes to get
to work?
Everything I know is that I have to use the joint probability density function.
probability statistics uniform-distribution
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
$endgroup$
add a comment |
$begingroup$
I have a problem with the following exercise:
X corresponds to the duration of Paul’s commute to work, and Y to the duration of Peter’s. X is uniformly distributed in [15, 25] and Y in [15, 30]. X and Y are assumed
to be independent.
What is the probability that Peter and Paul both take more than 20 minutes to get
to work?
Everything I know is that I have to use the joint probability density function.
probability statistics uniform-distribution
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
$endgroup$
add a comment |
$begingroup$
I have a problem with the following exercise:
X corresponds to the duration of Paul’s commute to work, and Y to the duration of Peter’s. X is uniformly distributed in [15, 25] and Y in [15, 30]. X and Y are assumed
to be independent.
What is the probability that Peter and Paul both take more than 20 minutes to get
to work?
Everything I know is that I have to use the joint probability density function.
probability statistics uniform-distribution
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
$endgroup$
I have a problem with the following exercise:
X corresponds to the duration of Paul’s commute to work, and Y to the duration of Peter’s. X is uniformly distributed in [15, 25] and Y in [15, 30]. X and Y are assumed
to be independent.
What is the probability that Peter and Paul both take more than 20 minutes to get
to work?
Everything I know is that I have to use the joint probability density function.
probability statistics uniform-distribution
probability statistics uniform-distribution
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
asked Dec 14 '18 at 16:04
HuckleberryHuckleberry
1
1
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint:
"Everything I know is that I have to use the joint probability density function..."
The independence of $X$ and $Y$ tells you the opposite.
You are asked to find: $$P(X>20,Y>20)$$ where ${X>20}$ and ${Y>20}$ are independent events.
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
$endgroup$
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
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%2f3039544%2fjoint-uniform-distribution-two-different-intervals%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
$begingroup$
Hint:
"Everything I know is that I have to use the joint probability density function..."
The independence of $X$ and $Y$ tells you the opposite.
You are asked to find: $$P(X>20,Y>20)$$ where ${X>20}$ and ${Y>20}$ are independent events.
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
$endgroup$
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
add a comment |
$begingroup$
Hint:
"Everything I know is that I have to use the joint probability density function..."
The independence of $X$ and $Y$ tells you the opposite.
You are asked to find: $$P(X>20,Y>20)$$ where ${X>20}$ and ${Y>20}$ are independent events.
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
$endgroup$
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
add a comment |
$begingroup$
Hint:
"Everything I know is that I have to use the joint probability density function..."
The independence of $X$ and $Y$ tells you the opposite.
You are asked to find: $$P(X>20,Y>20)$$ where ${X>20}$ and ${Y>20}$ are independent events.
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
$endgroup$
Hint:
"Everything I know is that I have to use the joint probability density function..."
The independence of $X$ and $Y$ tells you the opposite.
You are asked to find: $$P(X>20,Y>20)$$ where ${X>20}$ and ${Y>20}$ are independent events.
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
answered Dec 14 '18 at 16:15
drhabdrhab
102k545136
102k545136
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
add a comment |
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Thanks for the hint. Now I'm totally unsure how I should proceed. I was thinking about using double integrals from '20 till infinity'....
$endgroup$
– Huckleberry
Dec 14 '18 at 16:47
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
$begingroup$
Can find $P(X>20)$ and $P(Y>20)$ separately? Then multiplication of these results gives you the answer on base of independence.
$endgroup$
– drhab
Dec 14 '18 at 17:08
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%2f3039544%2fjoint-uniform-distribution-two-different-intervals%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
