Mixing
Probability. Solving equation with distribution function
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 '18 at 8:08
Atstovas
987
|
show 5 more comments
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 '18 at 8:08
Atstovas
987
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33
|
show 5 more comments
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
asked Nov 21 '18 at 8:08
Atstovas
987
Distribution function is given
$$D(x)= begin{cases}0, text{ if } x<0 \ frac{x}{5}+frac{1}{5} text{ if } 0 leq x <3 \ 1, text{ if } x geq 3 end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $pin(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Nov 21 '18 at 8:08
Atstovas
987
asked Nov 21 '18 at 8:08
Atstovas
987
asked Nov 21 '18 at 8:08
Atstovas
987
asked Nov 21 '18 at 8:08
Atstovas
987
asked Nov 21 '18 at 8:08
Atstovas
987
987
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33
|
show 5 more comments
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33
|
show 5 more comments
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%2f3007415%2fprobability-solving-equation-with-distribution-function%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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3007415%2fprobability-solving-equation-with-distribution-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
Are there jumps in the cumulative distribution function? If so, where and how big?
– Henry
Nov 21 '18 at 8:25
You should check whether your suggested $D_2$ is a cumulative distribution function or a probability density function
– Henry
Nov 21 '18 at 8:27
yes. when x=0 and x=3, jump is 1/5
– Atstovas
Nov 21 '18 at 8:27
and $D_2= 1/5 text{ when } x in [0,3) text{ and }0 text{ otherwise } $
– Atstovas
Nov 21 '18 at 8:30
So your suggested $D_2$ is not a cumulative distribution function (it is not increasing and does not approach $1$); nor is it a probability density function (its integral is not $1$)
– Henry
Nov 21 '18 at 8:33