Probability of null set
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
add a comment |
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
probability
asked Nov 18 at 14:59
user587389
326
326
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
2
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
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%2f3003638%2fprobability-of-null-set%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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%2f3003638%2fprobability-of-null-set%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
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19