Limits of a density functionWriting the density of a continuous random variable in terms of a...
How do you catch Smeargle in Pokemon Go?
Looking for a specific 6502 Assembler
Why does 0.-5 evaluate to -5?
Is "the fire consumed everything on its way" correct?
I have trouble understanding this fallacy: "If A, then B. Therefore if not-B, then not-A."
What is the difference between rolling more dice versus fewer dice?
What will happen if Parliament votes "no" on each of the Brexit-related votes to be held on the 12th, 13th and 14th of March?
Limits of a density function
How does one write from a minority culture? A question on cultural references
Why zero tolerance on nudity in space?
Why are all my replica super soldiers young adults or old teenagers?
How to assess the long-term stability of a college as part of a job search
How do I prevent a homebrew Grappling Hook feature from trivializing Tomb of Annihilation?
Short story where statues have their heads replaced by those of carved insect heads
Is using an 'empty' metaphor considered bad style?
Changing the laptop's CPU. Should I reinstall Linux?
Has any human ever had the choice to leave Earth permanently?
Current across a wire with zero potential difference
Why does magnet wire need to be insulated?
Is there a verb that means to inject with poison?
How do you voice extended chords?
Does diversity provide anything that meritocracy does not?
Early credit roll before the end of the film
Is there a lava-breathing lizard creature (that could be worshipped by a cult) in 5e?
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
