Limits of a density functionWriting the density of a continuous random variable in terms of a...
Why was Lupin comfortable with saying Voldemort's name?
How do you voice extended chords?
False written accusations not made public - is there law to cover this?
Why is it that Bernie Sanders is always called a "socialist"?
Why does 0.-5 evaluate to -5?
Early credit roll before the end of the film
Explanation of a regular pattern only occuring for prime numbers
What is the wife of a henpecked husband called?
Separate environment for personal and development use under macOS
Is there a verb that means to inject with poison?
Removing whitespace between consecutive numbers
Citing paywalled articles accessed via illegal web sharing
A starship is travelling at 0.9c and collides with a small rock. Will it leave a clean hole through, or will more happen?
Do "fields" always combine by addition?
Is "the fire consumed everything on its way" correct?
Why didn't Tom Riddle take the presence of Fawkes and the Sorting Hat as more of a threat?
Why did Luke use his left hand to shoot?
How to access internet and run apt-get through a middle server?
TikZ graph edges not drawn nicely
How to visualize the Riemann-Roch theorem from complex analysis or geometric topology considerations?
Why did Democrats in the Senate oppose the Born-Alive Abortion Survivors Protection Act (2019 S.130)?
How to politely refuse in-office gym instructor for steroids and protein
How do I append a character to the end of every line in an excel cell?
Why would space fleets be aligned?
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
