Limits of a density functionWriting the density of a continuous random variable in terms of a...
Building an exterior wall within an exterior wall for insulation
What is the wife of a henpecked husband called?
I have trouble understanding this fallacy: "If A, then B. Therefore if not-B, then not-A."
How do I prevent a homebrew Grappling Hook feature from trivializing Tomb of Annihilation?
How do you voice extended chords?
How to politely refuse in-office gym instructor for steroids and protein
How to visualize the Riemann-Roch theorem from complex analysis or geometric topology considerations?
Why are the books in the Game of Thrones citadel library shelved spine inwards?
Removing whitespace between consecutive numbers
Eww, those bytes are gross
Why does magnet wire need to be insulated?
Non-Cancer terminal illness that can affect young (age 10-13) girls?
How to access internet and run apt-get through a middle server?
How to deal with possible delayed baggage?
A Missing Symbol for This Logo
What makes papers publishable in top-tier journals?
Is a new boolean field better than null reference when a value can be meaningfully absent?
Why was Lupin comfortable with saying Voldemort's name?
Cat is tipping over bed-side lamps during the night
Why does photorec keep finding files after I have filled the disk free space as root?
Do "fields" always combine by addition?
Citing paywalled articles accessed via illegal web sharing
How to not let the Identify spell spoil everything?
Does diversity provide anything that meritocracy does not?
Limits of a density function
Writing the density of a continuous random variable in terms of a probabilityCriteria to select the number of neighbors in the k-th-nearest-neighbor density estimationExpectation of density ratio of two iid variablesFind the mode of a probability distribution functionProbability density function of transformed variableProve f(x) is a probability density function (pdf)Interpretation of the hazard rate and the probability density functionHow can I show that Uniform($0,A$) ,as $A to infty$, is an improper denisty?Parzen density estimates convergenceSymmetric probability density function proof
$begingroup$
If the limit of a density function exists does it the follow that it is zero? To put is formally
$$exists a in mathbb R lim_{t rightarrow infty} f(t) = a Rightarrow a= 0.$$
asked 4 hours ago
Jesper HybelJesper Hybel
921614
$endgroup$
add a comment |
$begingroup$
If the limit of a density function exists does it the follow that it is zero? To put is formally
$$exists a in mathbb R lim_{t rightarrow infty} f(t) = a Rightarrow a= 0.$$
asked 4 hours ago
Jesper HybelJesper Hybel
921614
$endgroup$
add a comment |
$begingroup$
If the limit of a density function exists does it the follow that it is zero? To put is formally
$$exists a in mathbb R lim_{t rightarrow infty} f(t) = a Rightarrow a= 0.$$
asked 4 hours ago
Jesper HybelJesper Hybel
921614
$endgroup$
If the limit of a density function exists does it the follow that it is zero? To put is formally
$$exists a in mathbb R lim_{t rightarrow infty} f(t) = a Rightarrow a= 0.$$
asked 4 hours ago
Jesper HybelJesper Hybel
921614
asked 4 hours ago
Jesper HybelJesper Hybel
921614
asked 4 hours ago
Jesper HybelJesper Hybel
921614
asked 4 hours ago
Jesper HybelJesper Hybel
921614
asked 4 hours ago
Jesper HybelJesper Hybel
921614
921614
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Yes.
Suppose the limit is anything else, so $lim_{t rightarrow infty} f(t) = a neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < frac{a}{2}$. In particular, $f(t) > frac{a}{2}$ in this reigon.
But then:
$$
int_{mathbf{R}} f(t) dt geq int_{N}^{infty} f(t) dt geq int_{N}^{infty} frac{a}{2} dt = infty
$$
So $f$ cannot be a density function.
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
$endgroup$
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: "65"
};
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
},
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%2fstats.stackexchange.com%2fquestions%2f394594%2flimits-of-a-density-function%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
$begingroup$
Yes.
Suppose the limit is anything else, so $lim_{t rightarrow infty} f(t) = a neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < frac{a}{2}$. In particular, $f(t) > frac{a}{2}$ in this reigon.
But then:
$$
int_{mathbf{R}} f(t) dt geq int_{N}^{infty} f(t) dt geq int_{N}^{infty} frac{a}{2} dt = infty
$$
So $f$ cannot be a density function.
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
$endgroup$
add a comment |
$begingroup$
Yes.
Suppose the limit is anything else, so $lim_{t rightarrow infty} f(t) = a neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < frac{a}{2}$. In particular, $f(t) > frac{a}{2}$ in this reigon.
But then:
$$
int_{mathbf{R}} f(t) dt geq int_{N}^{infty} f(t) dt geq int_{N}^{infty} frac{a}{2} dt = infty
$$
So $f$ cannot be a density function.
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
$endgroup$
add a comment |
$begingroup$
Yes.
Suppose the limit is anything else, so $lim_{t rightarrow infty} f(t) = a neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < frac{a}{2}$. In particular, $f(t) > frac{a}{2}$ in this reigon.
But then:
$$
int_{mathbf{R}} f(t) dt geq int_{N}^{infty} f(t) dt geq int_{N}^{infty} frac{a}{2} dt = infty
$$
So $f$ cannot be a density function.
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
$endgroup$
Yes.
Suppose the limit is anything else, so $lim_{t rightarrow infty} f(t) = a neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < frac{a}{2}$. In particular, $f(t) > frac{a}{2}$ in this reigon.
But then:
$$
int_{mathbf{R}} f(t) dt geq int_{N}^{infty} f(t) dt geq int_{N}^{infty} frac{a}{2} dt = infty
$$
So $f$ cannot be a density function.
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
edited 2 hours ago
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
answered 3 hours ago
Matthew DruryMatthew Drury
25.8k262104
25.8k262104
add a comment |
add a comment |
Thanks for contributing an answer to Cross Validated!
- 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%2fstats.stackexchange.com%2fquestions%2f394594%2flimits-of-a-density-function%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
