Functions of uniform density
$begingroup$
Consider the random variable X with the uniform
density having $α = 1$ and $β = 3$.
(a) Use the result of Example 2 to find the probability
density of $Y = |X|$
In example two they showed that such a function(Y=|X|) would have the density of the form:
$g(y) = begin{cases} f(y) + f(-y) space text{for} space y>0 \ 0 space text{elsewhere} end{cases}$
I have learnt two techinques, distribution function technique and transformation in one variable technique.
The answer given in the book:
$frac{1}{8} y^{−3/4} $ for $ 0 < y < 1$ and
$g(y) =frac{1}{4}$ for $1 <y < 3$
I'm totally lost in this question
Shouldn't there be distribution only for $1<y<3$? Why is $0<y<1$ there?
Even if both are there I'm not getting anything close to the two given answers, just getting weird answers like 1 and 1/2
random-variables
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
$endgroup$
add a comment |
$begingroup$
Consider the random variable X with the uniform
density having $α = 1$ and $β = 3$.
(a) Use the result of Example 2 to find the probability
density of $Y = |X|$
In example two they showed that such a function(Y=|X|) would have the density of the form:
$g(y) = begin{cases} f(y) + f(-y) space text{for} space y>0 \ 0 space text{elsewhere} end{cases}$
I have learnt two techinques, distribution function technique and transformation in one variable technique.
The answer given in the book:
$frac{1}{8} y^{−3/4} $ for $ 0 < y < 1$ and
$g(y) =frac{1}{4}$ for $1 <y < 3$
I'm totally lost in this question
Shouldn't there be distribution only for $1<y<3$? Why is $0<y<1$ there?
Even if both are there I'm not getting anything close to the two given answers, just getting weird answers like 1 and 1/2
random-variables
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
$endgroup$
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32
add a comment |
$begingroup$
Consider the random variable X with the uniform
density having $α = 1$ and $β = 3$.
(a) Use the result of Example 2 to find the probability
density of $Y = |X|$
In example two they showed that such a function(Y=|X|) would have the density of the form:
$g(y) = begin{cases} f(y) + f(-y) space text{for} space y>0 \ 0 space text{elsewhere} end{cases}$
I have learnt two techinques, distribution function technique and transformation in one variable technique.
The answer given in the book:
$frac{1}{8} y^{−3/4} $ for $ 0 < y < 1$ and
$g(y) =frac{1}{4}$ for $1 <y < 3$
I'm totally lost in this question
Shouldn't there be distribution only for $1<y<3$? Why is $0<y<1$ there?
Even if both are there I'm not getting anything close to the two given answers, just getting weird answers like 1 and 1/2
random-variables
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
$endgroup$
Consider the random variable X with the uniform
density having $α = 1$ and $β = 3$.
(a) Use the result of Example 2 to find the probability
density of $Y = |X|$
In example two they showed that such a function(Y=|X|) would have the density of the form:
$g(y) = begin{cases} f(y) + f(-y) space text{for} space y>0 \ 0 space text{elsewhere} end{cases}$
I have learnt two techinques, distribution function technique and transformation in one variable technique.
The answer given in the book:
$frac{1}{8} y^{−3/4} $ for $ 0 < y < 1$ and
$g(y) =frac{1}{4}$ for $1 <y < 3$
I'm totally lost in this question
Shouldn't there be distribution only for $1<y<3$? Why is $0<y<1$ there?
Even if both are there I'm not getting anything close to the two given answers, just getting weird answers like 1 and 1/2
random-variables
random-variables
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
edited Dec 3 '18 at 11:28
Sumukh Sai
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
asked Dec 3 '18 at 10:54
Sumukh SaiSumukh Sai
206
206
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32
add a comment |
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32
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
});
}
});
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%2f3023904%2ffunctions-of-uniform-density%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
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%2f3023904%2ffunctions-of-uniform-density%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
$begingroup$
What do you think how the distribution of $X$ looks like? And what is the result of example 2?
$endgroup$
– callculus
Dec 3 '18 at 11:00
$begingroup$
Apologies, have now put in info about example 2
$endgroup$
– Sumukh Sai
Dec 3 '18 at 11:14
$begingroup$
Looks to me the distribution of $|X|$ is the same as that of $X$. Have you quoted the question correctly?
$endgroup$
– StubbornAtom
Dec 3 '18 at 12:24
$begingroup$
The question is quoted correctly
$endgroup$
– Sumukh Sai
Dec 3 '18 at 12:32