Mixing
How $F_n$ is related to $F_{n+1}$
$begingroup$
A researcher has computed the empirical distribution $F_n$ for a data set $x_1, x_2, . . . , x_n$. She discovers an extra data point, $x_{n+1}$. She wonders how $F_n$ is related to $F_{n+1}$, the empirical distribution function for the new data set. Which of the following statements is correct?
a) $F_{n+1}(x)=F_n(x)− frac{1}{n+1}:for:−∞<x<∞$
b) $F_{n+1}(x)=F_n(x)+ frac{1}{n+1}:for:−∞<x<∞$
c) $F_{n+1}(x_n) ≤ F_n(x_n):if:x_n > x_{n+1}$
d) $F_{n+1}(x_2) ≤ F_n(x_2):if:x_2 < x_{n+1}$
e) $F_{n+1}(x) = F_n(x):if:x > x_{n+1}$
f) $F_{n+1}(x) = F_n(x):if:x < x_{n+1}$
I have no clue how to find the correct answer (D) can someone help me?
probability
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
$endgroup$
add a comment |
$begingroup$
A researcher has computed the empirical distribution $F_n$ for a data set $x_1, x_2, . . . , x_n$. She discovers an extra data point, $x_{n+1}$. She wonders how $F_n$ is related to $F_{n+1}$, the empirical distribution function for the new data set. Which of the following statements is correct?
a) $F_{n+1}(x)=F_n(x)− frac{1}{n+1}:for:−∞<x<∞$
b) $F_{n+1}(x)=F_n(x)+ frac{1}{n+1}:for:−∞<x<∞$
c) $F_{n+1}(x_n) ≤ F_n(x_n):if:x_n > x_{n+1}$
d) $F_{n+1}(x_2) ≤ F_n(x_2):if:x_2 < x_{n+1}$
e) $F_{n+1}(x) = F_n(x):if:x > x_{n+1}$
f) $F_{n+1}(x) = F_n(x):if:x < x_{n+1}$
I have no clue how to find the correct answer (D) can someone help me?
probability
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
$endgroup$
1
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
2
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
2
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51
add a comment |
$begingroup$
A researcher has computed the empirical distribution $F_n$ for a data set $x_1, x_2, . . . , x_n$. She discovers an extra data point, $x_{n+1}$. She wonders how $F_n$ is related to $F_{n+1}$, the empirical distribution function for the new data set. Which of the following statements is correct?
a) $F_{n+1}(x)=F_n(x)− frac{1}{n+1}:for:−∞<x<∞$
b) $F_{n+1}(x)=F_n(x)+ frac{1}{n+1}:for:−∞<x<∞$
c) $F_{n+1}(x_n) ≤ F_n(x_n):if:x_n > x_{n+1}$
d) $F_{n+1}(x_2) ≤ F_n(x_2):if:x_2 < x_{n+1}$
e) $F_{n+1}(x) = F_n(x):if:x > x_{n+1}$
f) $F_{n+1}(x) = F_n(x):if:x < x_{n+1}$
I have no clue how to find the correct answer (D) can someone help me?
probability
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
$endgroup$
A researcher has computed the empirical distribution $F_n$ for a data set $x_1, x_2, . . . , x_n$. She discovers an extra data point, $x_{n+1}$. She wonders how $F_n$ is related to $F_{n+1}$, the empirical distribution function for the new data set. Which of the following statements is correct?
a) $F_{n+1}(x)=F_n(x)− frac{1}{n+1}:for:−∞<x<∞$
b) $F_{n+1}(x)=F_n(x)+ frac{1}{n+1}:for:−∞<x<∞$
c) $F_{n+1}(x_n) ≤ F_n(x_n):if:x_n > x_{n+1}$
d) $F_{n+1}(x_2) ≤ F_n(x_2):if:x_2 < x_{n+1}$
e) $F_{n+1}(x) = F_n(x):if:x > x_{n+1}$
f) $F_{n+1}(x) = F_n(x):if:x < x_{n+1}$
I have no clue how to find the correct answer (D) can someone help me?
probability
probability
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
asked Jan 22 at 17:37
Mark JaconMark Jacon
1127
1127
1
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
2
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
2
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51
add a comment |
1
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
2
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
2
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51
1
1
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
2
2
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
2
2
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51
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%2f3083443%2fhow-f-n-is-related-to-f-n1%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%2f3083443%2fhow-f-n-is-related-to-f-n1%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
1
$begingroup$
The relation is $F_n+F_{n+1}=F_{n+2}$, if you ask Fibonacci:)
$endgroup$
– Dietrich Burde
Jan 22 at 17:55
2
$begingroup$
@DietrichBurde Nonsense.
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:13
2
$begingroup$
Mark, use the definition: en.wikipedia.org/wiki/Empirical_distribution_function
$endgroup$
– Jean-Claude Arbaut
Jan 22 at 18:16
$begingroup$
Ok I'll try thanks
$endgroup$
– Mark Jacon
Jan 22 at 18:51